Encoder that determines an intra prediction mode used for a current block and performs quantization on first transform coefficients or second transform coefficients based on whether a primary transform basis is included in predetermined transform bases

ABSTRACT

An encoder that encodes a video includes a processor and memory. Using the memory, the processor: derives a prediction error of an image included in the video, by subtracting a prediction image of the image from the image; determines a secondary transform basis based on a primary transform basis, the primary transform basis being a transform basis for a primary transform to be performed on the prediction error, the secondary transform basis being a transform basis for a secondary transform to be performed on a result of the primary transform; performs the primary transform on the prediction error using the primary transform basis; performs the secondary transform on a result of the primary transform using the secondary transform basis; performs quantization on a result of the secondary transform; and encodes a result of the quantization as data of the image.

BACKGROUND 1. Technical Field

The present disclosure relates to an encoder etc. that encodes a video.

2. Description of the Related Art

Conventionally, as a standard for coding a video, there is H.265 that isalso referred to as high efficiency video coding (HEVC) (see, H.265(ISO/IEC 23008-2 HEVC)/HEVC (High Efficiency Video Coding)).

SUMMARY

An encoder according to one aspect of the present disclosure is anencoder that encodes a video, and includes a processor and memory. Usingthe memory, the processor: derives a prediction error of an imageincluded in the video, by subtracting a prediction image of the imagefrom the image; determines a secondary transform basis based on aprimary transform basis, the primary transform basis being a transformbasis for a primary transform to be performed on the prediction error,the secondary transform basis being a transform basis for a secondarytransform to be performed on a result of the primary transform; performsthe primary transform on the prediction error using the primarytransform basis; performs the secondary transform on a result of theprimary transform using the secondary transform basis; performsquantization on a result of the secondary transform; and encodes aresult of the quantization as data of the image.

It should be noted that these general or specific aspects may beimplemented by a system, a device, a method, an integrated circuit, acomputer program, or a non-transitory computer-readable recording mediumsuch as a compact disc read only memory (CD-ROM), or by any combinationof systems, devices, methods, integrated circuits, computer programs, orrecording media.

BRIEF DESCRIPTION OF DRAWINGS

These and other objects, advantages and features of the disclosure willbecome apparent from the following description thereof taken inconjunction with the accompanying drawings that illustrate a specificembodiment of the present disclosure.

FIG. 1 is a block diagram illustrating a functional configuration of anencoder according to Embodiment 1.

FIG. 2 illustrates one example of block splitting according toEmbodiment 1.

FIG. 3 is a chart indicating transform basis functions for eachtransform type.

FIG. 4A illustrates one example of a filter shape used in Adaptive LoopFiltering (ALF).

FIG. 4B illustrates another example of a filter shape used in ALF.

FIG. 4C illustrates another example of a filter shape used in ALF.

FIG. 5A illustrates 67 intra prediction modes used in intra prediction.

FIG. 5B is a flow chart for illustrating an outline of a predictionimage correction process performed via Overlapped Block MotionCompensation (OBMC) processing.

FIG. 5C is a conceptual diagram for illustrating an outline of aprediction image correction process performed via OBMC processing.

FIG. 5D illustrates one example of Frame Rate Up-Conversion (FRUC).

FIG. 6 is for illustrating pattern matching (bilateral matching) betweentwo blocks along a motion trajectory.

FIG. 7 is for illustrating pattern matching (template matching) betweena template in the current picture and a block in a reference picture.

FIG. 8 is for illustrating a model assuming uniform linear motion.

FIG. 9A is for illustrating deriving a motion vector of each sub-blockbased on motion vectors of neighboring blocks.

FIG. 9B is for illustrating an outline of a process for deriving amotion vector via merge mode.

FIG. 9C is a conceptual diagram for illustrating an outline ofDecoder-Side Motion Vector Refinement (DMVR) processing.

FIG. 9D is for illustrating an outline of a prediction image generationmethod using a luminance correction process performed via LocalIllumination Compression (LIC) processing.

FIG. 10 is a block diagram illustrating a functional configuration of adecoder according to Embodiment 1.

FIG. 11 is a flow chart illustrating selection of a secondary transformbasis based on a primary transform basis.

FIG. 12 is a relationship diagram illustrating the first specificexample of an association between separable primary transform basiscandidates and non-separable secondary transform basis candidates.

FIG. 13 is a relationship diagram illustrating the second specificexample of an association between separable primary transform basiscandidates and non-separable secondary transform basis candidates.

FIG. 14 is a relationship diagram illustrating the third specificexample of an association between separable primary transform basiscandidates and non-separable secondary transform basis candidates.

FIG. 15 is a relationship diagram illustrating the fourth specificexample of an association between separable primary transform basiscandidates and non-separable secondary transform basis candidates.

FIG. 16 is a relationship diagram illustrating the fifth specificexample of an association between separable primary transform basiscandidates and non-separable secondary transform basis candidates.

FIG. 17 is a relationship diagram illustrating the first specificexample of an association between separable primary transform basiscandidates and separable secondary transform basis candidates.

FIG. 18 is a relationship diagram illustrating the second specificexample of an association between separable primary transform basiscandidates and separable secondary transform basis candidates.

FIG. 19 is a relationship diagram illustrating a specific example of anassociation between non-separable primary transform basis candidates andnon-separable secondary transform basis candidates.

FIG. 20 is a relationship diagram illustrating a specific example of anassociation between non-separable primary transform basis candidates andseparable secondary transform basis candidates.

FIG. 21 is a relationship diagram illustrating a specific example of anassociation between primary transform basis candidates and secondarytransform basis candidates in a state in which separable transforms andnon-separable transforms are present.

FIG. 22 is a flow chart illustrating selection of a secondary transformbasis based on a primary transform basis and an intra prediction mode.

FIG. 23 is a relationship diagram illustrating a specific example of anassociation between intra prediction modes, separable primary transformbasis candidates, and non-separable secondary transform basiscandidates.

FIG. 24 is a block diagram illustrating an implementation example of anencoder according to Embodiment 1.

FIG. 25 is a flow chart illustrating an example of operations performedby the encoder according to Embodiment 1.

FIG. 26 is a block diagram illustrating an implementation example of adecoder according to Embodiment 1.

FIG. 27 is a flow chart illustrating an example of operations performedby the decoder according to Embodiment 1.

FIG. 28 illustrates an overall configuration of a content providingsystem for implementing a content distribution service.

FIG. 29 illustrates one example of an encoding structure in scalableencoding.

FIG. 30 illustrates one example of an encoding structure in scalableencoding.

FIG. 31 illustrates an example of a display screen of a web page.

FIG. 32 illustrates an example of a display screen of a web page.

FIG. 33 illustrates an example of a smartphone.

FIG. 34 is a block diagram illustrating a configuration example of asmartphone.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(Underlying Knowledge Forming Basis of the Present Disclosure)

For example, when an encoder encodes a video, the encoder derives aprediction error by subtracting a prediction image from an imageincluded in the video. Next, the encoder performs a frequency transformand quantization on the prediction error, and encodes the results asdata of the image.

In a natural image, the amount of high frequency components isrelatively small. Accordingly, a frequency transform concentratesinformation in the low frequency side, thereby enabling efficientcoding. In addition, quantization removes the relatively small amount ofhigh frequency components, thereby reducing the amount of information.The high frequency components have a small impact on image quality, sothe negative effects of the deterioration in the image quality aresmall.

For example, since the amount of high frequency components is relativelysmall, a frequency transform and quantization successively generatecoefficients having a value of 0 in the high frequency region. Here, acoefficient having a value of 0 is referred to as a zero coefficient,and a coefficient having a value other than 0 is referred to as anonzero coefficient. The encoder can reduce the coding amount of zerocoefficients generated successively. Accordingly, the encoder can reducethe total coding amount by performing the frequency transform andquantization.

Moreover, the encoder may perform a secondary transform after thefrequency transform and before the quantization so that more zerocoefficients are generated successively. In this case, the frequencytransform is also expressed as a primary transform. The primarytransform is not limited to a frequency transform, and may be anorthogonal transform etc. The secondary transform is basically theorthogonal transform.

In other words, the encoder may perform the primary transform, thesecondary transform, and the quantization on the prediction error. Thereis a possibility of further reducing the coding amount by performing thesecondary transform in addition to the primary transform.

A decoder performs operations equivalent to those performed by theencoder. Specifically, the decoder decodes the data of the image. Next,the decoder performs inverse quantization, an inverse secondarytransform, and an inverse primary transform on the data of the image.Then, the decoder derives the image by adding, as the prediction error,the results of the inverse quantization, the inverse secondarytransform, and the inverse primary transform to the prediction image.

However, if the secondary transform is not performed properly, there isa possibility that the number of zero coefficients generatedsuccessively does not increase. Stated differently, if the secondarytransform is not performed properly, it is difficult to reduce thecoding amount.

In view of this, for example, an encoder according to one aspect of thepresent disclosure is an encoder that encodes a video, and includes aprocessor and memory. Using the memory, the processor: derives aprediction error of an image included in the video, by subtracting aprediction image of the image from the image; determines a secondarytransform basis based on a primary transform basis, the primarytransform basis being a transform basis for a primary transform to beperformed on the prediction error, the secondary transform basis being atransform basis for a secondary transform to be performed on a result ofthe primary transform; performs the primary transform on the predictionerror using the primary transform basis; performs the secondarytransform on a result of the primary transform using the secondarytransform basis; performs quantization on a result of the secondarytransform; and encodes a result of the quantization as data of theimage.

With this, the encoder can perform the primary transform and thesecondary transform using the appropriate combination of the primarytransform basis and the secondary transform basis. For this reason, theencoder can properly perform processing relating to transform.Accordingly, the encoder can perform encoding efficiently based on thecontinuity of zero coefficients.

Moreover, for example, the processor determines the secondary transformbasis based on the primary transform basis and a parameter encoded whenthe processor encodes the video.

With this, the encoder can perform the primary transform and thesecondary transform using the appropriate combination of the primarytransform basis, the secondary transform basis, and the parameterencoded.

Moreover, for example, the parameter indicates an intra prediction mode,and the processor determines the secondary transform basis based on theprimary transform basis and the intra prediction mode indicated by theparameter.

With this, the encoder can perform the primary transform and thesecondary transform using the appropriate combination of the primarytransform basis, the secondary transform basis, and the intra predictionmode.

Moreover, for example, the processor: determines the primary transformbasis from among a plurality of primary transform basis candidates; anddetermines the secondary transform basis from among at least onesecondary transform basis candidate associated with a primary transformbasis candidate determined as the primary transform basis among theplurality of primary transform basis candidates.

With this, the encoder can adaptively determine the secondary transformbasis from among the at least one secondary transform basis candidateassociated with the primary transform basis.

Moreover, for example, at least two of the plurality of primarytransform basis candidates are associated with a common secondarytransform basis candidate.

This standardizes and simplifies the processing. Accordingly, it ispossible to reduce the processing resources.

Moreover, for example, a total number of the at least one secondarytransform basis candidate associated with the primary transform basiscandidate depends on the primary transform basis candidate.

With this, the total number of the at least one secondary transformbasis candidate can be appropriately determined based on the primarytransform basis candidate.

Moreover, for example, the secondary transform basis determined when theprimary transform basis is a combination of a first transform basis fora vertical direction and a second transform basis for a horizontaldirection is identical to the secondary transform basis determined whenthe primary transform basis is a combination of the second transformbasis for the vertical direction and the first transform basis for thehorizontal direction.

With this, the encoder can use the common secondary transform basis forthe two primary transform bases having an inverse relationship betweenthe vertical direction and the horizontal direction. It is assumed thatthe characteristics of these two primary transform bases will not changesignificantly. Accordingly, even when the encoder uses the commonsecondary transform basis for the two primary transform bases, theencoder can properly perform the primary transform and the secondarytransform on the two primary transform bases.

Moreover, for example, the secondary transform basis determined when theprimary transform basis is a combination of a first transform basis fora vertical direction and a second transform basis for a horizontaldirection is a transform basis obtained by transposing the secondarytransform basis determined when the primary transform basis is acombination of the second transform basis for the vertical direction andthe first transform basis for the horizontal direction.

With this, the encoder can use the two secondary transform bases one ofwhich is obtained by transposing the other, for the two primarytransform bases having an inverse relationship between the verticaldirection and the horizontal direction. It is assumed that verticalcharacteristics and horizontal characteristics have been transposed inthe two primary transform bases. Accordingly, by using the two secondarytransform bases, one of which is obtained by transposing the other, forthe two primary transform bases, the encoder can properly perform theprimary transform and the secondary transform.

Moreover, for example, when the secondary transform basis is acombination of a transform basis for a vertical direction and atransform basis for a horizontal direction, the transform basis for thevertical direction and the transform basis for the horizontal directionare identical.

This standardizes and simplifies the processing. Accordingly, it ispossible to reduce the processing resources.

Moreover, for example, when there is only one secondary transform basiscandidate associated with a primary transform basis candidate determinedas the primary transform basis, the processor avoids encodinginformation indicating the secondary transform basis determined.

With this, the encoder can reduce the amount of information encoded whenthe secondary transform basis is uniquely determined. Accordingly, it ispossible to reduce the coding amount.

Moreover, for example, when a total number of transform basis candidatesfor one of information indicating the primary transform basis andinformation indicating the secondary transform basis is limited to one,the processor encodes only the other of the information indicating theprimary transform basis and the information indicating the secondarytransform basis.

With this, the encoder can reduce the amount of information encoded,compared to a case in which both the information indicating the primarytransform basis and the information indicating the secondary transformbasis are encoded. Accordingly, it is possible to reduce the codingamount.

Moreover, for example, the secondary transform basis is a transformbasis learned based on the primary transform basis.

With this, the encoder can use the secondary transform basis obtainedbased on the characteristics of the primary transform basis.Accordingly, the encoder can properly perform the primary transform andthe secondary transform.

Moreover, for example, when the secondary transform basis is a separabletransform basis, the processor performs a separable transform as thesecondary transform, and when the secondary transform basis is anon-separable transform basis, the processor performs a non-separabletransform as the secondary transform.

With this, the encoder can adaptively switch between the separablesecondary transform and the non-separable secondary transform.

Moreover, for example, the processor determines whether to perform thesecondary transform, and the secondary transform basis when thesecondary transform is performed, based on the primary transform basis.

With this, the encoder can properly determine whether to perform thesecondary transform, based on the primary transform basis. In addition,the encoder can properly determine the secondary transform basis whenthe secondary transform is performed, based on the primary transformbasis.

Moreover, for example, each of the primary transform and the secondarytransform is a separable transform or a non-separable transform, and theprocessor: (i) separates the primary transform into a plurality ofdirectional primary transforms, and performs the primary transform byperforming the plurality of directional primary transforms, or (ii)performs the primary transform without separating the primary transforminto the plurality of directional primary transforms; and (i) separatesthe secondary transform into a plurality of directional secondarytransforms, and performs the secondary transform by performing theplurality of directional secondary transforms, or (ii) performs thesecondary transform without separating the secondary transform into theplurality of directional secondary transforms.

With this, the encoder can separate the primary transform into a primarytransform for the vertical direction and a primary transform for thehorizontal direction, and can perform both the primary transform for thevertical direction and the primary transform for the horizontaldirection. Alternatively, the encoder can perform the primary transformwithout dividing the primary transform into a primary transform for thevertical direction and a primary transform for the horizontal direction.Further, the encoder can separate the secondary transform into asecondary transform for the vertical direction and a secondary transformfor the horizontal direction, and can perform both the secondarytransform for the vertical direction and the secondary transform for thehorizontal direction. Alternatively, the encoder can perform thesecondary transform without dividing the secondary transform into asecondary transform for the vertical direction and a secondary transformfor the horizontal direction.

For example, a decoder according to one aspect of the present disclosureis a decoder that decodes a video, and includes a processor; and memory.Using the memory, the processor: decodes data of an image included inthe video; performs inverse quantization on the data; determines aninverse secondary transform basis based on an inverse primary transformbasis, the inverse primary transform basis being a transform basis foran inverse primary transform to be performed on a result of an inversesecondary transform, the inverse secondary transform basis being atransform basis for the inverse secondary transform to be performed on aresult of the inverse quantization; performs the inverse secondarytransform on a result of the inverse quantization using the inversesecondary transform basis; performs the inverse primary transform on aresult of the inverse secondary transform using the inverse primarytransform basis; and derives the image by adding a result of the inverseprimary transform as a prediction error of the image to a predictionimage of the image.

With this, the decoder can perform the inverse primary transform and theinverse secondary transform using the appropriate combination of theinverse primary transform basis and the inverse secondary transformbasis. For this reason, the decoder can properly perform processingrelating to transform. Accordingly, the decoder can perform decodingefficiently based on the continuity of zero coefficients.

Moreover, for example, the processor determines the inverse secondarytransform basis based on the inverse primary transform basis and aparameter decoded when the processor decodes the video.

With this, the decoder can perform the inverse primary transform and theinverse secondary transform using the appropriate combination of theinverse primary transform basis, the inverse secondary transform basis,and a parameter decoded.

Moreover, for example, the parameter indicates an intra prediction mode,and the processor determines the inverse secondary transform basis basedon the inverse primary transform basis and the intra prediction modeindicated by the parameter.

With this, the decoder can perform the inverse primary transform and theinverse secondary transform using the appropriate combination of theinverse primary transform basis, the inverse secondary transform basis,and the intra prediction mode.

Moreover, for example, the processor: determines the inverse primarytransform basis from among a plurality of inverse primary transformbasis candidates; and determines the inverse secondary transform basisfrom among at least one inverse secondary transform basis candidateassociated with an inverse primary transform basis candidate determinedas the inverse primary transform basis among the plurality of inverseprimary transform basis candidates.

With this, the decoder can adaptively determine the inverse secondarytransform basis from among the at least one inverse secondary transformbasis candidate associated with the inverse primary transform basis.

Moreover, for example, at least two of the plurality of inverse primarytransform basis candidates are associated with a common inversesecondary transform basis candidate.

This standardizes and simplifies the processing. Accordingly, it ispossible to reduce the processing resources.

Moreover, for example, a total number of the at least one inversesecondary transform basis candidate associated with the inverse primarytransform basis candidate depends on the inverse primary transform basiscandidate.

With this, the total number of the at least one inverse secondarytransform basis candidate can be appropriately determined based on theinverse primary transform basis candidate.

Moreover, for example, the inverse secondary transform basis determinedwhen the inverse primary transform basis is a combination of a firsttransform basis for a vertical direction and a second transform basisfor a horizontal direction is identical to the inverse secondarytransform basis determined when the inverse primary transform basis is acombination of the second transform basis for the vertical direction andthe first transform basis for the horizontal direction.

With this, the decoder can use the common inverse secondary transformbasis for the two inverse primary transform bases having an inverserelationship between the vertical direction and the horizontaldirection. It is assumed that the characteristics of these two inverseprimary transform bases will not change significantly. Accordingly, evenwhen the decoder uses the common inverse secondary transform basis forthe two inverse primary transform bases, the decoder can properlyperform the inverse primary transform and the inverse secondarytransform.

Moreover, for example, the inverse secondary transform basis determinedwhen the inverse primary transform basis is a combination of a firsttransform basis for a vertical direction and a second transform basisfor a horizontal direction is a transform basis obtained by transposingthe inverse secondary transform basis determined when the inverseprimary transform basis is a combination of the second transform basisfor the vertical direction and the first transform basis for thehorizontal direction.

With this, the decoder can use the two inverse secondary transform basesone of which is obtained by transposing the other, for the two inverseprimary transform bases having an inverse relationship between thevertical direction and the horizontal direction. It is assumed thatvertical characteristics and horizontal characteristics have beentransposed in the two inverse primary transform bases. Accordingly, byusing the two inverse secondary transform bases, one of which isobtained by transposing the other, for the two inverse primary transformbases, the decoder can properly perform the inverse primary transformand the inverse secondary transform.

Moreover, for example, when the inverse secondary transform basis is acombination of a transform basis for a vertical direction and atransform basis for a horizontal direction, the transform basis for thevertical direction and the transform basis for the horizontal directionare identical.

This standardizes and simplifies the processing. Accordingly, it ispossible to reduce the processing resources.

Moreover, for example, when there is only one inverse secondarytransform basis candidate associated with an inverse primary transformbasis candidate determined as the inverse primary transform basis, theprocessor avoids decoding information indicating the inverse secondarytransform basis determined.

With this, the decoder can reduce the amount of information decoded whenthe inverse secondary transform basis is uniquely determined.Accordingly, it is possible to reduce the coding amount.

Moreover, for example, when a total number of transform basis candidatesfor one of information indicating the inverse primary transform basisand information indicating the inverse secondary transform basis islimited to one, the processor decodes only the other of the informationindicating the inverse primary transform basis and the informationindicating the inverse secondary transform basis.

With this, the decoder can reduce the amount of information decoded,compared to a case in which both the information indicating the inverseprimary transform basis and the information indicating the inversesecondary transform basis are decoded. Accordingly, it is possible toreduce the coding amount.

Moreover, for example, the inverse secondary transform basis is atransform basis learned based on the inverse primary transform basis.

With this, the decoder can use the inverse secondary transform basisobtained based on the characteristics of the inverse primary transformbasis. Accordingly, the decoder can properly perform the inverse primarytransform and the inverse secondary transform.

Moreover, for example, when the inverse secondary transform basis is aseparable inverse transform basis, the processor performs a separableinverse transform as the inverse secondary transform, and when theinverse secondary transform basis is a non-separable inverse transformbasis, the processor performs a non-separable inverse transform as theinverse secondary transform.

With this, the decoder can adaptively switch between the separableinverse secondary transform and the non-separable inverse secondarytransform.

Moreover, for example, the processor determines whether to perform theinverse secondary transform, and the inverse secondary transform basiswhen the inverse secondary transform is performed, based on the inverseprimary transform basis.

With this, the decoder can properly determine whether to perform theinverse secondary transform, based on the inverse primary transformbasis. In addition, the decoder can properly determine the inversesecondary transform basis when the inverse secondary transform isperformed, based on the inverse primary transform basis.

Moreover, for example, each of the inverse primary transform and theinverse secondary transform is a separable inverse transform or anon-separable inverse transform, and the processor: (i) separates theinverse primary transform into a plurality of directional inverseprimary transforms, and performs the inverse primary transform byperforming the plurality of directional inverse primary transforms, or(ii) performs the inverse primary transform without separating theinverse primary transform into the plurality of directional inverseprimary transforms; and (i) separates the inverse secondary transforminto a plurality of directional inverse secondary transforms, andperforms the inverse secondary transform by performing the plurality ofdirectional inverse secondary transforms, or (ii) performs the inversesecondary transform without separating the inverse secondary transforminto the plurality of directional inverse secondary transforms.

With this, the decoder can separate the inverse primary transform intoan inverse primary transform for the vertical direction and an inverseprimary transform for the horizontal direction, and can perform both theinverse primary transform for the vertical direction and the inverseprimary transform for the horizontal direction. Alternatively, thedecoder can perform the inverse primary transform without dividing theinverse primary transform into an inverse primary transform for thevertical direction and an inverse primary transform for the horizontaldirection. Further, the decoder can separate the inverse secondarytransform into an inverse secondary transform for the vertical directionand an inverse secondary transform for the horizontal direction, and canperform both the inverse secondary transform for the vertical directionand the inverse secondary transform for the horizontal direction.Alternatively, the decoder can perform the inverse secondary transformwithout dividing the inverse secondary transform into an inversesecondary transform for the vertical direction and an inverse secondarytransform for the horizontal direction.

For example, an encoding method according to one aspect of the presentdisclosure is an encoding method of encoding a video, the encodingmethod including: deriving a prediction error of an image included inthe video, by subtracting a prediction image of the image from theimage; determining a secondary transform basis based on a primarytransform basis, the primary transform basis being a transform basis fora primary transform to be performed on the prediction error, thesecondary transform basis being a transform basis for a secondarytransform to be performed on a result of the primary transform;performing the primary transform on the prediction error using theprimary transform basis; performing the secondary transform on a resultof the primary transform using the secondary transform basis; performingquantization on a result of the secondary transform; and encoding aresult of the quantization as data of the image.

With this, it is possible to perform the primary transform and thesecondary transform using the appropriate combination of the primarytransform basis and the secondary transform basis. For this reason, itis possible to properly perform processing relating to transform.Accordingly, it is possible to efficiency perform encoding based on thecontinuity of zero coefficients.

For example, a decoding method according to one aspect of the presentdisclosure is a decoding method of decoding a video, the decoding methodincluding: decoding data of an image included in the video; performinginverse quantization on the data; determining an inverse secondarytransform basis based on an inverse primary transform basis, the inverseprimary transform basis being a transform basis for an inverse primarytransform to be performed on a result of an inverse secondary transform,the inverse secondary transform basis being a transform basis for theinverse secondary transform to be performed on a result of the inversequantization; performing the inverse secondary transform on a result ofthe inverse quantization using the inverse secondary transform basis;performing the inverse primary transform on a result of the inversesecondary transform using the inverse primary transform basis; andderiving the image by adding a result of the inverse primary transformas a prediction error of the image to a prediction image of the image.

With this, it is possible to perform the inverse primary transform andthe inverse secondary transform using the appropriate combination of theinverse primary transform basis and the inverse secondary transformbasis. For this reason, it is possible to properly perform processingrelating to transform. Accordingly, it is possible to efficiency performdecoding based on the continuity of zero coefficients.

Furthermore, these general or specific aspects may be implemented by asystem, a device, a method, an integrated circuit, a computer program,or a non-transitory computer-readable recording medium such as a compactdisc read only memory (CD-ROM), or by any combination of systems,devices, methods, integrated circuits, computer programs, or recordingmedia.

Hereinafter, embodiments will be described specifically with referenceto the drawings.

It should be noted that the embodiments described below each show ageneral or specific example. The numerical values, shapes, materials,components, the arrangement and connection of the components, steps,order of the steps, etc., indicated in the following embodiments aremere examples, and therefore are not intended to limit the scope of theclaims. Further, among the components in the following embodiments,those not recited in any of the independent claims defining the broadestgeneric concepts are described as optional components.

Embodiment 1

First, an outline of Embodiment 1 will be presented. Embodiment 1 is oneexample of an encoder and a decoder to which the processes and/orconfigurations presented in subsequent description of aspects of thepresent disclosure are applicable. Note that Embodiment 1 is merely oneexample of an encoder and a decoder to which the processes and/orconfigurations presented in the description of aspects of the presentdisclosure are applicable. The processes and/or configurations presentedin the description of aspects of the present disclosure can also beimplemented in an encoder and a decoder different from those accordingto Embodiment 1.

When the processes and/or configurations presented in the description ofaspects of the present disclosure are applied to Embodiment 1, forexample, any of the following may be performed.

(1) regarding the encoder or the decoder according to Embodiment 1,among components included in the encoder or the decoder according toEmbodiment 1, substituting a component corresponding to a componentpresented in the description of aspects of the present disclosure with acomponent presented in the description of aspects of the presentdisclosure;

(2) regarding the encoder or the decoder according to Embodiment 1,implementing discretionary changes to functions or implemented processesperformed by one or more components included in the encoder or thedecoder according to Embodiment 1, such as addition, substitution, orremoval, etc., of such functions or implemented processes, thensubstituting a component corresponding to a component presented in thedescription of aspects of the present disclosure with a componentpresented in the description of aspects of the present disclosure;

(3) regarding the method implemented by the encoder or the decoderaccording to Embodiment 1, implementing discretionary changes such asaddition of processes and/or substitution, removal of one or more of theprocesses included in the method, and then substituting a processescorresponding to a process presented in the description of aspects ofthe present disclosure with a process presented in the description ofaspects of the present disclosure;

(4) combining one or more components included in the encoder or thedecoder according to Embodiment 1 with a component presented in thedescription of aspects of the present disclosure, a component includingone or more functions included in a component presented in thedescription of aspects of the present disclosure, or a component thatimplements one or more processes implemented by a component presented inthe description of aspects of the present disclosure;

(5) combining a component including one or more functions included inone or more components included in the encoder or the decoder accordingto Embodiment 1, or a component that implements one or more processesimplemented by one or more components included in the encoder or thedecoder according to Embodiment 1 with a component presented in thedescription of aspects of the present disclosure, a component includingone or more functions included in a component presented in thedescription of aspects of the present disclosure, or a component thatimplements one or more processes implemented by a component presented inthe description of aspects of the present disclosure;

(6) regarding the method implemented by the encoder or the decoderaccording to Embodiment 1, among processes included in the method,substituting a process corresponding to a process presented in thedescription of aspects of the present disclosure with a processpresented in the description of aspects of the present disclosure; and

(7) combining one or more processes included in the method implementedby the encoder or the decoder according to Embodiment 1 with a processpresented in the description of aspects of the present disclosure.

Note that the implementation of the processes and/or configurationspresented in the description of aspects of the present disclosure is notlimited to the above examples. For example, the processes and/orconfigurations presented in the description of aspects of the presentdisclosure may be implemented in a device used for a purpose differentfrom the moving picture/picture encoder or the moving picture/picturedecoder disclosed in Embodiment 1. Moreover, the processes and/orconfigurations presented in the description of aspects of the presentdisclosure may be independently implemented. Moreover, processes and/orconfigurations described in different aspects may be combined.

[Encoder Outline]

First, the encoder according to Embodiment 1 will be outlined. FIG. 1 isa block diagram illustrating a functional configuration of encoder 100according to Embodiment 1. Encoder 100 is a moving picture/pictureencoder that encodes a moving picture/picture block by block.

As illustrated in FIG. 1 , encoder 100 is a device that encodes apicture block by block, and includes splitter 102, subtractor 104,transformer 106, quantizer 108, entropy encoder 110, inverse quantizer112, inverse transformer 114, adder 116, block memory 118, loop filter120, frame memory 122, intra predictor 124, inter predictor 126, andprediction controller 128.

Encoder 100 is realized as, for example, a generic processor and memory.In this case, when a software program stored in the memory is executedby the processor, the processor functions as splitter 102, subtractor104, transformer 106, quantizer 108, entropy encoder 110, inversequantizer 112, inverse transformer 114, adder 116, loop filter 120,intra predictor 124, inter predictor 126, and prediction controller 128.Alternatively, encoder 100 may be realized as one or more dedicatedelectronic circuits corresponding to splitter 102, subtractor 104,transformer 106, quantizer 108, entropy encoder 110, inverse quantizer112, inverse transformer 114, adder 116, loop filter 120, intrapredictor 124, inter predictor 126, and prediction controller 128.

Hereinafter, each component included in encoder 100 will be described.

[Splitter]

Splitter 102 splits each picture included in an input moving pictureinto blocks, and outputs each block to subtractor 104. For example,splitter 102 first splits a picture into blocks of a fixed size (forexample, 128×128). The fixed size block is also referred to as codingtree unit (CTU). Splitter 102 then splits each fixed size block intoblocks of variable sizes (for example, 64×64 or smaller), based onrecursive quadtree and/or binary tree block splitting. The variable sizeblock is also referred to as a coding unit (CU), a prediction unit (PU),or a transform unit (TU). Note that in this embodiment, there is no needto differentiate between CU, PU, and TU; all or some of the blocks in apicture may be processed per CU, PU, or TU.

FIG. 2 illustrates one example of block splitting according toEmbodiment 1. In FIG. 2 , the solid lines represent block boundaries ofblocks split by quadtree block splitting, and the dashed lines representblock boundaries of blocks split by binary tree block splitting.

Here, block 10 is a square 128×128 pixel block (128×128 block). This128×128 block 10 is first split into four square 64×64 blocks (quadtreeblock splitting).

The top left 64×64 block is further vertically split into two rectangle32×64 blocks, and the left 32×64 block is further vertically split intotwo rectangle 16×64 blocks (binary tree block splitting). As a result,the top left 64×64 block is split into two 16×64 blocks 11 and 12 andone 32×64 block 13.

The top right 64×64 block is horizontally split into two rectangle 64×32blocks 14 and 15 (binary tree block splitting).

The bottom left 64×64 block is first split into four square 32×32 blocks(quadtree block splitting). The top left block and the bottom rightblock among the four 32×32 blocks are further split. The top left 32×32block is vertically split into two rectangle 16×32 blocks, and the right16×32 block is further horizontally split into two 16×16 blocks (binarytree block splitting). The bottom right 32×32 block is horizontallysplit into two 32×16 blocks (binary tree block splitting). As a result,the bottom left 64×64 block is split into 16×32 block 16, two 16×16blocks 17 and 18, two 32×32 blocks 19 and 20, and two 32×16 blocks 21and 22.

The bottom right 64×64 block 23 is not split.

As described above, in FIG. 2 , block 10 is split into 13 variable sizeblocks 11 through 23 based on recursive quadtree and binary tree blocksplitting. This type of splitting is also referred to as quadtree plusbinary tree (QTBT) splitting.

Note that in FIG. 2 , one block is split into four or two blocks(quadtree or binary tree block splitting), but splitting is not limitedto this example. For example, one block may be split into three blocks(ternary block splitting). Splitting including such ternary blocksplitting is also referred to as multi-type tree (MBT) splitting.

[Subtractor]

Subtractor 104 subtracts a prediction signal (prediction sample) from anoriginal signal (original sample) per block split by splitter 102. Inother words, subtractor 104 calculates prediction errors (also referredto as residuals) of a block to be encoded (hereinafter referred to as acurrent block). Subtractor 104 then outputs the calculated predictionerrors to transformer 106.

The original signal is a signal input into encoder 100, and is a signalrepresenting an image for each picture included in a moving picture (forexample, a luma signal and two chroma signals). Hereinafter, a signalrepresenting an image is also referred to as a sample.

[Transformer]

Transformer 106 transforms spatial domain prediction errors intofrequency domain transform coefficients, and outputs the transformcoefficients to quantizer 108. More specifically, transformer 106applies, for example, a predefined discrete cosine transform (DCT) ordiscrete sine transform (DST) to spatial domain prediction errors.

Note that transformer 106 may adaptively select a transform type fromamong a plurality of transform types, and transform prediction errorsinto transform coefficients by using a transform basis functioncorresponding to the selected transform type. This sort of transform isalso referred to as explicit multiple core transform (EMT) or adaptivemultiple transform (AMT).

The transform types include, for example, DCT-II, DCT-V, DCT-VIII,DST-I, and DST-VII. FIG. 3 is a chart indicating transform basisfunctions for each transform type. In FIG. 3 , N indicates the number ofinput pixels. For example, selection of a transform type from among theplurality of transform types may depend on the prediction type (intraprediction and inter prediction), and may depend on intra predictionmode.

Information indicating whether to apply such EMT or AMT (referred to as,for example, an AMT flag) and information indicating the selectedtransform type is signalled at the CU level. Note that the signaling ofsuch information need not be performed at the CU level, and may beperformed at another level (for example, at the sequence level, picturelevel, slice level, tile level, or CTU level).

Moreover, transformer 106 may apply a secondary transform to thetransform coefficients (transform result). Such a secondary transform isalso referred to as adaptive secondary transform (AST) or non-separablesecondary transform (NSST). For example, transformer 106 applies asecondary transform to each sub-block (for example, each 4×4 sub-block)included in the block of the transform coefficients corresponding to theintra prediction errors. Information indicating whether to apply NSSTand information related to the transform matrix used in NSST aresignalled at the CU level. Note that the signaling of such informationneed not be performed at the CU level, and may be performed at anotherlevel (for example, at the sequence level, picture level, slice level,tile level, or CTU level).

Here, a separable transform is a method in which a transform isperformed a plurality of times by separately performing a transform foreach direction according to the number of dimensions input. Anon-separable transform is a method of performing a collective transformin which two or more dimensions in a multidimensional input arecollectively regarded as a single dimension.

In one example of a non-separable transform, when the input is a 4×4block, the 4×4 block is regarded as a single array including 16components, and the transform applies a 16×16 transform matrix to thearray.

Moreover, similar to above, after an input 4×4 block is regarded as asingle array including 16 components, a transform that performs aplurality of Givens rotations on the array (i.e., a Hypercube-GivensTransform) is also one example of a non-separable transform.

[Quantizer]

Quantizer 108 quantizes the transform coefficients output fromtransformer 106. More specifically, quantizer 108 scans, in apredetermined scanning order, the transform coefficients of the currentblock, and quantizes the scanned transform coefficients based onquantization parameters (QP) corresponding to the transformcoefficients. Quantizer 108 then outputs the quantized transformcoefficients (hereinafter referred to as quantized coefficients) of thecurrent block to entropy encoder 110 and inverse quantizer 112.

A predetermined order is an order for quantizing/inverse quantizingtransform coefficients. For example, a predetermined scanning order isdefined as ascending order of frequency (from low to high frequency) ordescending order of frequency (from high to low frequency).

A quantization parameter is a parameter defining a quantization stepsize (quantization width). For example, if the value of the quantizationparameter increases, the quantization step size also increases. In otherwords, if the value of the quantization parameter increases, thequantization error increases.

[Entropy Encoder]

Entropy encoder 110 generates an encoded signal (encoded bitstream) byvariable length encoding quantized coefficients, which are inputs fromquantizer 108. More specifically, entropy encoder 110, for example,binarizes quantized coefficients and arithmetic encodes the binarysignal.

[Inverse Quantizer]

Inverse quantizer 112 inverse quantizes quantized coefficients, whichare inputs from quantizer 108. More specifically, inverse quantizer 112inverse quantizes, in a predetermined scanning order, quantizedcoefficients of the current block. Inverse quantizer 112 then outputsthe inverse quantized transform coefficients of the current block toinverse transformer 114.

[Inverse Transformer]

Inverse transformer 114 restores prediction errors by inversetransforming transform coefficients, which are inputs from inversequantizer 112. More specifically, inverse transformer 114 restores theprediction errors of the current block by applying an inverse transformcorresponding to the transform applied by transformer 106 on thetransform coefficients. Inverse transformer 114 then outputs therestored prediction errors to adder 116.

Note that since information is lost in quantization, the restoredprediction errors do not match the prediction errors calculated bysubtractor 104. In other words, the restored prediction errors includequantization errors.

[Adder]

Adder 116 reconstructs the current block by summing prediction errors,which are inputs from inverse transformer 114, and prediction samples,which are inputs from prediction controller 128. Adder 116 then outputsthe reconstructed block to block memory 118 and loop filter 120. Areconstructed block is also referred to as a local decoded block.

[Block Memory]

Block memory 118 is storage for storing blocks in a picture to beencoded (hereinafter referred to as a current picture) for reference inintra prediction. More specifically, block memory 118 storesreconstructed blocks output from adder 116.

[Loop Filter]

Loop filter 120 applies a loop filter to blocks reconstructed by adder116, and outputs the filtered reconstructed blocks to frame memory 122.A loop filter is a filter used in an encoding loop (in-loop filter), andincludes, for example, a deblocking filter (DF), a sample adaptiveoffset (SAO), and an adaptive loop filter (ALF).

In ALF, a least square error filter for removing compression artifactsis applied. For example, one filter from among a plurality of filters isselected for each 2×2 sub-block in the current block based on directionand activity of local gradients, and is applied.

More specifically, first, each sub-block (for example, each 2×2sub-block) is categorized into one out of a plurality of classes (forexample, 15 or 25 classes). The classification of the sub-block is basedon gradient directionality and activity. For example, classificationindex C is derived based on gradient directionality D (for example, 0 to2 or 0 to 4) and gradient activity A (for example, 0 to 4) (for example,C=5D+A). Then, based on classification index C, each sub-block iscategorized into one out of a plurality of classes (for example, 15 or25 classes).

For example, gradient directionality D is calculated by comparinggradients of a plurality of directions (for example, the horizontal,vertical, and two diagonal directions). Moreover, for example, gradientactivity A is calculated by summing gradients of a plurality ofdirections and quantizing the sum.

The filter to be used for each sub-block is determined from among theplurality of filters based on the result of such categorization.

The filter shape to be used in ALF is, for example, a circular symmetricfilter shape. FIG. 4A through FIG. 4C illustrate examples of filtershapes used in ALF. FIG. 4A illustrates a 5×5 diamond shape filter, FIG.4B illustrates a 7×7 diamond shape filter, and FIG. 4C illustrates a 9×9diamond shape filter. Information indicating the filter shape issignalled at the picture level. Note that the signaling of informationindicating the filter shape need not be performed at the picture level,and may be performed at another level (for example, at the sequencelevel, slice level, tile level, CTU level, or CU level).

The enabling or disabling of ALF is determined at the picture level orCU level. For example, for luma, the decision to apply ALF or not isdone at the CU level, and for chroma, the decision to apply ALF or notis done at the picture level. Information indicating whether ALF isenabled or disabled is signalled at the picture level or CU level. Notethat the signaling of information indicating whether ALF is enabled ordisabled need not be performed at the picture level or CU level, and maybe performed at another level (for example, at the sequence level, slicelevel, tile level, or CTU level).

The coefficients set for the plurality of selectable filters (forexample, 15 or 25 filters) is signalled at the picture level. Note thatthe signaling of the coefficients set need not be performed at thepicture level, and may be performed at another level (for example, atthe sequence level, slice level, tile level, CTU level, CU level, orsub-block level).

[Frame Memory]

Frame memory 122 is storage for storing reference pictures used in interprediction, and is also referred to as a frame buffer. Morespecifically, frame memory 122 stores reconstructed blocks filtered byloop filter 120.

[Intra Predictor]

Intra predictor 124 generates a prediction signal (intra predictionsignal) by intra predicting the current block with reference to a blockor blocks in the current picture and stored in block memory 118 (alsoreferred to as intra frame prediction). More specifically, intrapredictor 124 generates an intra prediction signal by intra predictionwith reference to samples (for example, luma and/or chroma values) of ablock or blocks neighboring the current block, and then outputs theintra prediction signal to prediction controller 128.

For example, intra predictor 124 performs intra prediction by using onemode from among a plurality of predefined intra prediction modes. Theintra prediction modes include one or more non-directional predictionmodes and a plurality of directional prediction modes.

The one or more non-directional prediction modes include, for example,planar prediction mode and DC prediction mode defined in theH.265/high-efficiency video coding (HEVC) standard (see NPL 1).

The plurality of directional prediction modes include, for example, the33 directional prediction modes defined in the H.265/HEVC standard. Notethat the plurality of directional prediction modes may further include32 directional prediction modes in addition to the 33 directionalprediction modes (for a total of 65 directional prediction modes). FIG.5A illustrates 67 intra prediction modes used in intra prediction (twonon-directional prediction modes and 65 directional prediction modes).The solid arrows represent the 33 directions defined in the H.265/HEVCstandard, and the dashed arrows represent the additional 32 directions.

Note that a luma block may be referenced in chroma block intraprediction. In other words, a chroma component of the current block maybe predicted based on a luma component of the current block. Such intraprediction is also referred to as cross-component linear model (CCLM)prediction. Such a chroma block intra prediction mode that references aluma block (referred to as, for example, CCLM mode) may be added as oneof the chroma block intra prediction modes.

Intra predictor 124 may correct post-intra-prediction pixel values basedon horizontal/vertical reference pixel gradients. Intra predictionaccompanied by this sort of correcting is also referred to as positiondependent intra prediction combination (PDPC). Information indicatingwhether to apply PDPC or not (referred to as, for example, a PDPC flag)is, for example, signalled at the CU level. Note that the signaling ofthis information need not be performed at the CU level, and may beperformed at another level (for example, on the sequence level, picturelevel, slice level, tile level, or CTU level).

[Inter Predictor]

Inter predictor 126 generates a prediction signal (inter predictionsignal) by inter predicting the current block with reference to a blockor blocks in a reference picture, which is different from the currentpicture and is stored in frame memory 122 (also referred to as interframe prediction). Inter prediction is performed per current block orper sub-block (for example, per 4×4 block) in the current block. Forexample, inter predictor 126 performs motion estimation in a referencepicture for the current block or sub-block. Inter predictor 126 thengenerates an inter prediction signal of the current block or sub-blockby motion compensation by using motion information (for example, amotion vector) obtained from motion estimation. Inter predictor 126 thenoutputs the generated inter prediction signal to prediction controller128.

The motion information used in motion compensation is signalled. Amotion vector predictor may be used for the signaling of the motionvector. In other words, the difference between the motion vector and themotion vector predictor may be signalled.

Note that the inter prediction signal may be generated using motioninformation for a neighboring block in addition to motion informationfor the current block obtained from motion estimation. Morespecifically, the inter prediction signal may be generated per sub-blockin the current block by calculating a weighted sum of a predictionsignal based on motion information obtained from motion estimation and aprediction signal based on motion information for a neighboring block.Such inter prediction (motion compensation) is also referred to asoverlapped block motion compensation (OBMC).

In such an OBMC mode, information indicating sub-block size for OBMC(referred to as, for example, OBMC block size) is signalled at thesequence level. Moreover, information indicating whether to apply theOBMC mode or not (referred to as, for example, an OBMC flag) issignalled at the CU level. Note that the signaling of such informationneed not be performed at the sequence level and CU level, and may beperformed at another level (for example, at the picture level, slicelevel, tile level, CTU level, or sub-block level).

Hereinafter, the OBMC mode will be described in further detail. FIG. 5Bis a flowchart and FIG. 5C is a conceptual diagram for illustrating anoutline of a prediction image correction process performed via OBMCprocessing.

First, a prediction image (Pred) is obtained through typical motioncompensation using a motion vector (MV) assigned to the current block.

Next, a prediction image (Pred_L) is obtained by applying a motionvector (MV_L) of the encoded neighboring left block to the currentblock, and a first pass of the correction of the prediction image ismade by superimposing the prediction image and Pred_L.

Similarly, a prediction image (Pred_U) is obtained by applying a motionvector (MV_U) of the encoded neighboring upper block to the currentblock, and a second pass of the correction of the prediction image ismade by superimposing the prediction image resulting from the first passand Pred_U. The result of the second pass is the final prediction image.

Note that the above example is of a two-pass correction method using theneighboring left and upper blocks, but the method may be a three-pass orhigher correction method that also uses the neighboring right and/orlower block.

Note that the region subject to superimposition may be the entire pixelregion of the block, and, alternatively, may be a partial block boundaryregion.

Note that here, the prediction image correction process is described asbeing based on a single reference picture, but the same applies when aprediction image is corrected based on a plurality of referencepictures. In such a case, after corrected prediction images resultingfrom performing correction based on each of the reference pictures areobtained, the obtained corrected prediction images are furthersuperimposed to obtain the final prediction image.

Note that the unit of the current block may be a prediction block and,alternatively, may be a sub-block obtained by further dividing theprediction block.

One example of a method for determining whether to implement OBMCprocessing is by using an obmc_flag, which is a signal that indicateswhether to implement OBMC processing. As one specific example, theencoder determines whether the current block belongs to a regionincluding complicated motion. The encoder sets the obmc_flag to a valueof “1” when the block belongs to a region including complicated motionand implements OBMC processing when encoding, and sets the obmc_flag toa value of “0” when the block does not belong to a region includingcomplication motion and encodes without implementing OBMC processing.The decoder switches between implementing OBMC processing or not bydecoding the obmc_flag written in the stream and performing the decodingin accordance with the flag value.

Note that the motion information may be derived on the decoder sidewithout being signalled. For example, a merge mode defined in theH.265/HEVC standard may be used. Moreover, for example, the motioninformation may be derived by performing motion estimation on thedecoder side. In this case, motion estimation is performed without usingthe pixel values of the current block.

Here, a mode for performing motion estimation on the decoder side willbe described. A mode for performing motion estimation on the decoderside is also referred to as pattern matched motion vector derivation(PMMVD) mode or frame rate up-conversion (FRUC) mode.

One example of FRUC processing is illustrated in FIG. 5D. First, acandidate list (a candidate list may be a merge list) of candidates eachincluding a motion vector predictor is generated with reference tomotion vectors of encoded blocks that spatially or temporally neighborthe current block. Next, the best candidate MV is selected from among aplurality of candidate MVs registered in the candidate list. Forexample, evaluation values for the candidates included in the candidatelist are calculated and one candidate is selected based on thecalculated evaluation values.

Next, a motion vector for the current block is derived from the motionvector of the selected candidate. More specifically, for example, themotion vector for the current block is calculated as the motion vectorof the selected candidate (best candidate MV), as-is. Alternatively, themotion vector for the current block may be derived by pattern matchingperformed in the vicinity of a position in a reference picturecorresponding to the motion vector of the selected candidate. In otherwords, when the vicinity of the best candidate MV is searched via thesame method and an MV having a better evaluation value is found, thebest candidate MV may be updated to the MV having the better evaluationvalue, and the MV having the better evaluation value may be used as thefinal MV for the current block. Note that a configuration in which thisprocessing is not implemented is also acceptable.

The same processes may be performed in cases in which the processing isperformed in units of sub-blocks.

Note that an evaluation value is calculated by calculating thedifference in the reconstructed image by pattern matching performedbetween a region in a reference picture corresponding to a motion vectorand a predetermined region. Note that the evaluation value may becalculated by using some other information in addition to thedifference.

The pattern matching used is either first pattern matching or secondpattern matching. First pattern matching and second pattern matching arealso referred to as bilateral matching and template matching,respectively.

In the first pattern matching, pattern matching is performed between twoblocks along the motion trajectory of the current block in two differentreference pictures. Therefore, in the first pattern matching, a regionin another reference picture conforming to the motion trajectory of thecurrent block is used as the predetermined region for theabove-described calculation of the candidate evaluation value.

FIG. 6 is for illustrating one example of pattern matching (bilateralmatching) between two blocks along a motion trajectory. As illustratedin FIG. 6 , in the first pattern matching, two motion vectors (MV0, MV1)are derived by finding the best match between two blocks along themotion trajectory of the current block (Cur block) in two differentreference pictures (Ref0, Ref1). More specifically, a difference between(i) a reconstructed image in a specified position in a first encodedreference picture (Ref0) specified by a candidate MV and (ii) areconstructed picture in a specified position in a second encodedreference picture (Ref1) specified by a symmetrical MV scaled at adisplay time interval of the candidate MV may be derived, and theevaluation value for the current block may be calculated by using thederived difference. The candidate MV having the best evaluation valueamong the plurality of candidate MVs may be selected as the final MV.

Under the assumption of continuous motion trajectory, the motion vectors(MV0, MV1) pointing to the two reference blocks shall be proportional tothe temporal distances (TD0, TD1) between the current picture (Cur Pic)and the two reference pictures (Ref0, Ref1). For example, when thecurrent picture is temporally between the two reference pictures and thetemporal distance from the current picture to the two reference picturesis the same, the first pattern matching derives a mirror basedbi-directional motion vector.

In the second pattern matching, pattern matching is performed between atemplate in the current picture (blocks neighboring the current block inthe current picture (for example, the top and/or left neighboringblocks)) and a block in a reference picture. Therefore, in the secondpattern matching, a block neighboring the current block in the currentpicture is used as the predetermined region for the above-describedcalculation of the candidate evaluation value.

FIG. 7 is for illustrating one example of pattern matching (templatematching) between a template in the current picture and a block in areference picture. As illustrated in FIG. 7 , in the second patternmatching, a motion vector of the current block is derived by searching areference picture (Rem) to find the block that best matches neighboringblocks of the current block (Cur block) in the current picture (CurPic). More specifically, a difference between (i) a reconstructed imageof an encoded region that is both or one of the neighboring left andneighboring upper region and (ii) a reconstructed picture in the sameposition in an encoded reference picture (Ref0) specified by a candidateMV may be derived, and the evaluation value for the current block may becalculated by using the derived difference. The candidate MV having thebest evaluation value among the plurality of candidate MVs may beselected as the best candidate MV.

Information indicating whether to apply the FRUC mode or not (referredto as, for example, a FRUC flag) is signalled at the CU level. Moreover,when the FRUC mode is applied (for example, when the FRUC flag is set totrue), information indicating the pattern matching method (first patternmatching or second pattern matching) is signalled at the CU level. Notethat the signaling of such information need not be performed at the CUlevel, and may be performed at another level (for example, at thesequence level, picture level, slice level, tile level, CTU level, orsub-block level).

Here, a mode for deriving a motion vector based on a model assuminguniform linear motion will be described. This mode is also referred toas a bi-directional optical flow (BIO) mode.

FIG. 8 is for illustrating a model assuming uniform linear motion. InFIG. 8 , (v_(x), v_(y)) denotes a velocity vector, and τ₀ and τ₁ denotetemporal distances between the current picture (Cur Pic) and tworeference pictures (Ref₀, Ref₁). (MVx₀, MVy₀) denotes a motion vectorcorresponding to reference picture Ref₀, and (MVx₁, MVy₁) denotes amotion vector corresponding to reference picture Ref₁.

Here, under the assumption of uniform linear motion exhibited byvelocity vector (v_(x), v_(y)), (MVx₀, MVy₀) and (MVx₁, MVy₁) arerepresented as (v_(x)τ₀, v_(y)τ₀) and (−v_(x)τ₁, −v_(y)τ₁),respectively, and the following optical flow equation is given.

$\begin{matrix}{{MATH}.1} &  \\{{{{\partial I^{(k)}}/{\partial t}} + {v_{x}{\partial I^{(k)}}/{\partial x}} + {v_{y}{\partial I^{(k)}}/{\partial y}}} = 0.} & (1)\end{matrix}$

Here, I^((k)) denotes a luma value from reference picture k (k=0, 1)after motion compensation. This optical flow equation shows that the sumof (i) the time derivative of the luma value, (ii) the product of thehorizontal velocity and the horizontal component of the spatial gradientof a reference picture, and (iii) the product of the vertical velocityand the vertical component of the spatial gradient of a referencepicture is equal to zero. A motion vector of each block obtained from,for example, a merge list is corrected pixel by pixel based on acombination of the optical flow equation and Hermite interpolation.

Note that a motion vector may be derived on the decoder side using amethod other than deriving a motion vector based on a model assuminguniform linear motion. For example, a motion vector may be derived foreach sub-block based on motion vectors of neighboring blocks.

Here, a mode in which a motion vector is derived for each sub-blockbased on motion vectors of neighboring blocks will be described. Thismode is also referred to as affine motion compensation prediction mode.

FIG. 9A is for illustrating deriving a motion vector of each sub-blockbased on motion vectors of neighboring blocks. In FIG. 9A, the currentblock includes 16 4×4 sub-blocks. Here, motion vector v₀ of the top leftcorner control point in the current block is derived based on motionvectors of neighboring sub-blocks, and motion vector v₁ of the top rightcorner control point in the current block is derived based on motionvectors of neighboring blocks. Then, using the two motion vectors v₀ andv₁, the motion vector (v_(x), v_(y)) of each sub-block in the currentblock is derived using Equation 2 below.

$\begin{matrix}{{MATH}.2} &  \\\left\{ \begin{matrix}{v_{x} = {{\frac{\left( {v_{1x} - v_{0x}} \right)}{w}x} - {\frac{\left( {v_{1y} - v_{0y}} \right)}{w}y} + v_{0x}}} \\{v_{y} = {{\frac{\left( {v_{1y} - v_{0y}} \right)}{w}x} + {\frac{\left( {v_{1x} - v_{0x}} \right)}{w}y} + v_{0y}}}\end{matrix} \right. & (2)\end{matrix}$

Here, x and y are the horizontal and vertical positions of thesub-block, respectively, and w is a predetermined weighted coefficient.

Such an affine motion compensation prediction mode may include a numberof modes of different methods of deriving the motion vectors of the topleft and top right corner control points. Information indicating such anaffine motion compensation prediction mode (referred to as, for example,an affine flag) is signalled at the CU level. Note that the signaling ofinformation indicating the affine motion compensation prediction modeneed not be performed at the CU level, and may be performed at anotherlevel (for example, at the sequence level, picture level, slice level,tile level, CTU level, or sub-block level).

[Prediction Controller]

Prediction controller 128 selects either the intra prediction signal orthe inter prediction signal, and outputs the selected prediction signalto subtractor 104 and adder 116.

Here, an example of deriving a motion vector via merge mode in a currentpicture will be given. FIG. 9B is for illustrating an outline of aprocess for deriving a motion vector via merge mode.

First, an MV predictor list in which candidate MV predictors areregistered is generated. Examples of candidate MV predictors include:spatially neighboring MV predictors, which are MVs of encoded blockspositioned in the spatial vicinity of the current block; a temporallyneighboring MV predictor, which is an MV of a block in an encodedreference picture that neighbors a block in the same location as thecurrent block; a combined MV predictor, which is an MV generated bycombining the MV values of the spatially neighboring MV predictor andthe temporally neighboring MV predictor; and a zero MV predictor, whichis an MV whose value is zero.

Next, the MV of the current block is determined by selecting one MVpredictor from among the plurality of MV predictors registered in the MVpredictor list.

Furthermore, in the variable-length encoder, a merge_idx, which is asignal indicating which MV predictor is selected, is written and encodedinto the stream.

Note that the MV predictors registered in the MV predictor listillustrated in FIG. 9B constitute one example. The number of MVpredictors registered in the MV predictor list may be different from thenumber illustrated in FIG. 9B, the MV predictors registered in the MVpredictor list may omit one or more of the types of MV predictors givenin the example in FIG. 9B, and the MV predictors registered in the MVpredictor list may include one or more types of MV predictors inaddition to and different from the types given in the example in FIG.9B.

Note that the final MV may be determined by performing DMVR processing(to be described later) by using the MV of the current block derived viamerge mode.

Here, an example of determining an MV by using DMVR processing will begiven.

FIG. 9C is a conceptual diagram for illustrating an outline of DMVRprocessing.

First, the most appropriate MVP set for the current block is consideredto be the candidate MV, reference pixels are obtained from a firstreference picture, which is a picture processed in the L0 direction inaccordance with the candidate MV, and a second reference picture, whichis a picture processed in the L1 direction in accordance with thecandidate MV, and a template is generated by calculating the average ofthe reference pixels.

Next, using the template, the surrounding regions of the candidate MVsof the first and second reference pictures are searched, and the MV withthe lowest cost is determined to be the final MV. Note that the costvalue is calculated using, for example, the difference between eachpixel value in the template and each pixel value in the regionssearched, as well as the MV value.

Note that the outlines of the processes described here are fundamentallythe same in both the encoder and the decoder.

Note that processing other than the processing exactly as describedabove may be used, so long as the processing is capable of deriving thefinal MV by searching the surroundings of the candidate MV.

Here, an example of a mode that generates a prediction image by usingLIC processing will be given.

FIG. 9D is for illustrating an outline of a prediction image generationmethod using a luminance correction process performed via LICprocessing.

First, an MV is extracted for obtaining, from an encoded referencepicture, a reference image corresponding to the current block.

Next, information indicating how the luminance value changed between thereference picture and the current picture is extracted and a luminancecorrection parameter is calculated by using the luminance pixel valuesfor the encoded left neighboring reference region and the encoded upperneighboring reference region, and the luminance pixel value in the samelocation in the reference picture specified by the MV.

The prediction image for the current block is generated by performing aluminance correction process by using the luminance correction parameteron the reference image in the reference picture specified by the MV.

Note that the shape of the surrounding reference region illustrated inFIG. 9D is just one example; the surrounding reference region may have adifferent shape.

Moreover, although a prediction image is generated from a singlereference picture in this example, in cases in which a prediction imageis generated from a plurality of reference pictures as well, theprediction image is generated after performing a luminance correctionprocess, via the same method, on the reference images obtained from thereference pictures.

One example of a method for determining whether to implement LICprocessing is by using an lic_flag, which is a signal that indicateswhether to implement LIC processing. As one specific example, theencoder determines whether the current block belongs to a region ofluminance change. The encoder sets the lic_flag to a value of “1” whenthe block belongs to a region of luminance change and implements LICprocessing when encoding, and sets the lic_flag to a value of “0” whenthe block does not belong to a region of luminance change and encodeswithout implementing LIC processing. The decoder switches betweenimplementing LIC processing or not by decoding the lic_flag written inthe stream and performing the decoding in accordance with the flagvalue.

One example of a different method of determining whether to implementLIC processing is determining so in accordance with whether LICprocessing was determined to be implemented for a surrounding block. Inone specific example, when merge mode is used on the current block,whether LIC processing was applied in the encoding of the surroundingencoded block selected upon deriving the MV in the merge mode processingmay be determined, and whether to implement LIC processing or not can beswitched based on the result of the determination. Note that in thisexample, the same applies to the processing performed on the decoderside.

[Decoder Outline]

Next, a decoder capable of decoding an encoded signal (encodedbitstream) output from encoder 100 will be described. FIG. 10 is a blockdiagram illustrating a functional configuration of decoder 200 accordingto Embodiment 1. Decoder 200 is a moving picture/picture decoder thatdecodes a moving picture/picture block by block.

As illustrated in FIG. 10 , decoder 200 includes entropy decoder 202,inverse quantizer 204, inverse transformer 206, adder 208, block memory210, loop filter 212, frame memory 214, intra predictor 216, interpredictor 218, and prediction controller 220.

Decoder 200 is realized as, for example, a generic processor and memory.In this case, when a software program stored in the memory is executedby the processor, the processor functions as entropy decoder 202,inverse quantizer 204, inverse transformer 206, adder 208, loop filter212, intra predictor 216, inter predictor 218, and prediction controller220. Alternatively, decoder 200 may be realized as one or more dedicatedelectronic circuits corresponding to entropy decoder 202, inversequantizer 204, inverse transformer 206, adder 208, loop filter 212,intra predictor 216, inter predictor 218, and prediction controller 220.

Hereinafter, each component included in decoder 200 will be described.

[Entropy Decoder]

Entropy decoder 202 entropy decodes an encoded bitstream. Morespecifically, for example, entropy decoder 202 arithmetic decodes anencoded bitstream into a binary signal. Entropy decoder 202 thendebinarizes the binary signal. With this, entropy decoder 202 outputsquantized coefficients of each block to inverse quantizer 204.

[Inverse Quantizer]

Inverse quantizer 204 inverse quantizes quantized coefficients of ablock to be decoded (hereinafter referred to as a current block), whichare inputs from entropy decoder 202. More specifically, inversequantizer 204 inverse quantizes quantized coefficients of the currentblock based on quantization parameters corresponding to the quantizedcoefficients. Inverse quantizer 204 then outputs the inverse quantizedcoefficients (i.e., transform coefficients) of the current block toinverse transformer 206.

[Inverse Transformer]

Inverse transformer 206 restores prediction errors by inversetransforming transform coefficients, which are inputs from inversequantizer 204.

For example, when information parsed from an encoded bitstream indicatesapplication of EMT or AMT (for example, when the AMT flag is set totrue), inverse transformer 206 inverse transforms the transformcoefficients of the current block based on information indicating theparsed transform type.

Moreover, for example, when information parsed from an encoded bitstreamindicates application of NSST, inverse transformer 206 applies asecondary inverse transform to the transform coefficients.

[Adder]

Adder 208 reconstructs the current block by summing prediction errors,which are inputs from inverse transformer 206, and prediction samples,which is an input from prediction controller 220. Adder 208 then outputsthe reconstructed block to block memory 210 and loop filter 212.

[Block Memory]

Block memory 210 is storage for storing blocks in a picture to bedecoded (hereinafter referred to as a current picture) for reference inintra prediction. More specifically, block memory 210 storesreconstructed blocks output from adder 208.

[Loop Filter]

Loop filter 212 applies a loop filter to blocks reconstructed by adder208, and outputs the filtered reconstructed blocks to frame memory 214and, for example, a display device.

When information indicating the enabling or disabling of ALF parsed froman encoded bitstream indicates enabled, one filter from among aplurality of filters is selected based on direction and activity oflocal gradients, and the selected filter is applied to the reconstructedblock.

[Frame Memory]

Frame memory 214 is storage for storing reference pictures used in interprediction, and is also referred to as a frame buffer. Morespecifically, frame memory 214 stores reconstructed blocks filtered byloop filter 212.

[Intra Predictor]

Intra predictor 216 generates a prediction signal (intra predictionsignal) by intra prediction with reference to a block or blocks in thecurrent picture and stored in block memory 210. More specifically, intrapredictor 216 generates an intra prediction signal by intra predictionwith reference to samples (for example, luma and/or chroma values) of ablock or blocks neighboring the current block, and then outputs theintra prediction signal to prediction controller 220.

Note that when an intra prediction mode in which a chroma block is intrapredicted from a luma block is selected, intra predictor 216 may predictthe chroma component of the current block based on the luma component ofthe current block.

Moreover, when information indicating the application of PDPC is parsedfrom an encoded bitstream, intra predictor 216 correctspost-intra-prediction pixel values based on horizontal/verticalreference pixel gradients.

[Inter Predictor]

Inter predictor 218 predicts the current block with reference to areference picture stored in frame memory 214. Inter prediction isperformed per current block or per sub-block (for example, per 4×4block) in the current block. For example, inter predictor 218 generatesan inter prediction signal of the current block or sub-block by motioncompensation by using motion information (for example, a motion vector)parsed from an encoded bitstream, and outputs the inter predictionsignal to prediction controller 220.

Note that when the information parsed from the encoded bitstreamindicates application of OBMC mode, inter predictor 218 generates theinter prediction signal using motion information for a neighboring blockin addition to motion information for the current block obtained frommotion estimation.

Moreover, when the information parsed from the encoded bitstreamindicates application of FRUC mode, inter predictor 218 derives motioninformation by performing motion estimation in accordance with thepattern matching method (bilateral matching or template matching) parsedfrom the encoded bitstream. Inter predictor 218 then performs motioncompensation using the derived motion information.

Moreover, when BIO mode is to be applied, inter predictor 218 derives amotion vector based on a model assuming uniform linear motion. Moreover,when the information parsed from the encoded bitstream indicates thataffine motion compensation prediction mode is to be applied, interpredictor 218 derives a motion vector of each sub-block based on motionvectors of neighboring blocks.

[Prediction Controller]

Prediction controller 220 selects either the intra prediction signal orthe inter prediction signal, and outputs the selected prediction signalto adder 208.

[Selection of Secondary Transform Basis]

The following describes selection of a secondary transform basis basedon a primary transform basis. For example, transformer 106 of encoder100 performs a transform on a prediction error, and performs are-transform on the result of the transform. Then, quantizer 108 ofencoder 100 performs quantization on the result of the re-transform. Thetransform performed on the prediction error is referred to as a primarytransform. The re-transform performed on the result of the transform isreferred to as a secondary transform. In other words, transformer 106performs the primary transform on the prediction error, and performs thesecondary transform on the result of the primary transform.

More specifically, transformer 106 performs the primary transform on theprediction error using a primary transform basis. Next, transformer 106performs the secondary transform on the result of the primary transformusing a secondary transform basis. The primary transform basis is atransform basis for the primary transform, and the secondary transformbasis is a transform basis for the secondary transform. For example, atransform basis includes data patterns. Each data pattern may bereferred to as a basis. In this case, the transform basis may beregarded as a basis set including bases.

For example, transformer 106 performs the primary transform on aprediction image by deriving, from a prediction image, a component valueof each data pattern of a primary transform basis. In other words, theresult of the primary transform is equivalent to the component valuesderived from the prediction image, and is equivalent to the componentvalues corresponding to the data patterns of the primary transformbasis.

Next, transformer 106 performs the secondary transform on the result ofthe primary transform by deriving, from the result of the primarytransform, a component value of each data pattern of a secondarytransform basis. In other words, the result of the secondary transformis equivalent to the component values derived from the result of theprimary transform, and is equivalent to the component valuescorresponding to the data patterns of the secondary transform basis.

Decoder 200 performs operations equivalent to those of encoder 100.Specifically, inverse transformer 206 of decoder 200 performs an inversesecondary transform on the result of inverse quantization using aninverse secondary transform basis. In addition, inverse transformer 206performs an inverse primary transform on the result of the inversesecondary transform using an inverse primary transform basis.

Here, the inverse primary transform is a transform inverse of theprimary transform. Decoder 200 derives data before the primary transformfrom data after the primary transform by performing the inverse primarytransform using the inverse primary transform basis. The inverse primarytransform basis is a transform basis for the inverse primary transform,and is a transform basis equivalent to the primary transform basis.

Specifically, decoder 200 may perform the inverse primary transform in aprocedure opposite to that of the primary transform, using the inverseprimary transform basis equivalent to the primary transform basis.

Moreover, the inverse secondary transform is a transform inverse of thesecondary transform. Decoder 200 derives data before the secondarytransform from data after the secondary transform by performing theinverse secondary transform using the inverse secondary transform basis.The inverse secondary transform basis is a transform basis for theinverse secondary transform, and is a transform basis equivalent to thesecondary transform basis.

Specifically, decoder 200 may perform the inverse secondary transform ina procedure opposite to that of the secondary transform, using theinverse secondary transform basis equivalent to the secondary transformbasis.

The result of the inverse quantization performed by decoder 200 isequivalent to the result of the secondary transform performed by encoder100. In other words, the result of the inverse quantization isequivalent to the component values derived from the result of theprimary transform, and is equivalent to the component valuescorresponding to the data patterns of the secondary transform basis. Forexample, when inverse transformer 206 performs the inverse secondarytransform on the result of the inverse quantization, inverse transformer206 derives the result of the primary transform by combining thesecomponent values using the inverse secondary transform basis.

Accordingly, the result of the inverse secondary transform is equivalentto the result of the primary transform performed by encoder 100. Inother words, the result of the inverse secondary transform is equivalentto the component values derived from the prediction image, and isequivalent to the component values corresponding to the data patterns ofthe primary transform basis. For example, when inverse transformer 206performs the inverse primary transform on the result of the inversesecondary transform, inverse transformer 206 derives a prediction errorby combining these component values using the inverse primary transformbasis.

Encoder 100 in the present embodiment determines the secondary transformbasis for use in the secondary transform based on the primary transformbasis for use in the primary transform. Similarly, decoder 200determines the inverse secondary transform basis for use in the inversesecondary transform based on the inverse primary transform basis for usein the inverse primary transform.

Although the following mainly describes encoder 100 as an example,decoder 200 operates in the same manner as encoder 100. In particular,inverse transformer 206 of decoder 200 operates in the same manner astransformer 106 of encoder 100. For example, the transform, primarytransform, secondary transform, primary transform basis, secondarytransform basis, etc. in the following description may be appropriatelyinterchangeable with the inverse transform, inverse primary transform,inverse secondary transform, inverse primary transform basis, inversesecondary transform basis, etc.

However, inverse transformer 206 of decoder 200 performs the inverseprimary transform after the inverse secondary transform. Encoder 100encodes information, and decoder 200 decodes the information. Forexample, when encoder 100 selects a transform basis based on a codingamount, a difference between an original image and a reconstructedimage, etc., encoder 100 encodes the information of the transform basis,and decoder 200 decodes the information of the transform basis.

FIG. 11 is a flow chart illustrating selection of a secondary transformbasis based on a primary transform basis. For example, transformer 106of encoder 100 illustrated in FIG. 1 performs the selection illustratedin FIG. 11 . Transformer 106 performs the selection of the secondarytransform basis based on the primary transform basis before performing asecondary transform. Transformer 106 may perform the selection of thesecondary transform basis not only immediately before the secondarytransform but also before a primary transform.

For example, transformer 106 selects a primary transform basis for eachblock or each unit of other data, and selects a secondary transformbasis based on the primary transform basis. Here, the block may be asub-block. In other words, in a loop of selecting a primary transformbasis, transformer 106 selects a secondary transform basis based on aprimary transform basis.

Specifically, first, transformer 106 selects a primary transform basis(S101). For example, transformer 106 selects a primary transform basisfrom among primary transform basis candidates that are candidates forthe primary transform basis. A primary transform basis candidate isbasically an orthogonal transform basis. Any orthogonal transform basiscan be used as a primary transform basis candidate.

For example, a primary transform basis candidate may be a transformbasis equivalent to DCT2 (DCT-II), DCT5 (DCT-V), DCT8 (DCT-VIII), DST1(DST-I), or DST7 (DST-VII).

Moreover, transformer 106 may select a primary transform basis based onan evaluation value. This evaluation value may be based on costevaluation called rate distortion (RD) cost, or may be specificallybased on a coding amount and a difference between an original image anda reconstructed image. For example, transformer 106 may calculate anevaluation value for each of primary transform basis candidates, andselect a primary transform basis candidate having the highest evaluationvalue as a primary transform basis from among the primary transformbasis candidates.

Alternatively, transformer 106 may select a primary transform basisbased on any coding parameter, such as a block size or intra predictionmode. For example, transformer 106 may select a primary transform basisassociated with a coding parameter.

Next, transformer 106 selects a secondary transform basis associatedwith the primary transform basis (S102). For example, transformer 106selects a secondary transform basis associated with the primarytransform basis from among secondary transform basis candidates that arecandidates for the secondary transform basis. A secondary transformbasis candidate is also basically an orthogonal transform basis. Anyorthogonal transform basis can be used as a secondary transform basiscandidate.

For example, a transform basis for Karhunen-Loeve (KL) transform may beoptimized by offline learning, or may be used as a secondary transformbasis candidate. In addition, in offline learning, training data may beselected on a condition based on an association between primarytransform basis candidates and secondary primary transform basiscandidates. For example, in offline learning of a secondary transformbasis candidate associated with a primary transform basis candidatecorresponding to DCT2, only the result of primary transform using DCT2may be used as training data.

A secondary transform basis candidate equivalent to the KL transform maybe determined based on training data, or may be associated with aprimary transform basis candidate used in selecting the training data.With this, transformer 106 can use the secondary transform basiscandidate updated based on the primary transform basis candidate byoffline learning. Accordingly, transformer 106 can properly perform thesecond transform on the result of the primary transform. As a result, itis possible to reduce a coding amount.

Alternatively, a secondary transform basis candidate equivalent to theKL transform may be determined by a primary transform result modelequivalent to a prediction error model based on a Gauss-Markov modeletc., or may be associated with a primary transform basis candidate usedin the primary transform. With this, transformer 106 can use thesecondary transform basis candidate determined based on the predictionerror model, the primary transform basis candidate, etc. Accordingly,transformer 106 can properly perform the second transform on the resultof the primary transform. As a result, it is possible to reduce a codingamount.

Moreover, transformer 106 can reduce an amount of processing byselecting a secondary transform basis associated with a primarytransform basis from among secondary transform basis candidates,compared to evaluating each of the secondary transform basis candidates.

In the above description, transformer 106 selects one primary transformbasis candidate as the primary transform basis from among the primarytransform basis candidates, and then selects the secondary transformbasis associated with the primary transform basis from among thesecondary transform basis candidates. However, these selections need notbe the final selections of the primary transform basis and the secondarytransform basis.

For example, by sequentially selecting a secondary transform basiscandidate based on an association between primary transform basiscandidates and secondary transform basis candidates while sequentiallyselecting a primary transform basis candidate, transformer 106 maysequentially select a combination of the primary transform basiscandidate and the secondary transform basis candidate. Next, transformer106 may derive an evaluation value, such as a RD cost, for eachcombination selected sequentially.

Then, transformer 106 may finally select the primary transform basiscandidate and the secondary transform basis candidate constituting thecombination having the best evaluation value, as a primary transformbasis and a secondary transform basis. Consequently, such a selectionresults in selecting the secondary transform basis based on the primarytransform basis.

Moreover, the KL transform may be used as the primary transform. Primarytransform basis candidates may each be a transform basis equivalent tothe KL transform, or may include a transform basis for the KL transform.

Moreover, the primary transform may be a separable transform, that is, aseparable primary transform. Alternatively, the primary transform may bea non-separable transform, that is, a non-separable primary transform.Likewise, the secondary transform may be a separable transform, that is,a separable secondary transform. Alternatively, the secondary transformmay be a non-separable transform, that is, a non-separable secondarytransform.

Moreover, a transform basis for the separable primary transform and atransform basis for the non-separable primary transform can be alsoexpressed as a separable primary transform basis and a non-separableprimary transform basis, respectively. In addition, their candidates canbe also expressed as a separable primary transform basis candidate and anon-separable primary transform basis candidate.

Moreover, a transform basis for the separable secondary transform and atransform basis for the non-separable secondary transform can be alsoexpressed as a separable secondary transform basis and a non-separablesecondary transform basis, respectively. In addition, their candidatescan be also expressed as a separable secondary transform basis candidateand a non-separable secondary transform basis candidate.

Similarly, the inverse primary transform may be a separable inversetransform, that is, a separable inverse primary transform.Alternatively, the inverse primary transform may be a non-separableinverse transform, that is, a non-separable inverse primary transform.Likewise, the inverse secondary transform may be a separable inversetransform, that is, a separable inverse secondary transform.Alternatively, the inverse secondary transform may be a non-separableinverse transform, that is, a non-separable inverse secondary transform.

Moreover, a transform basis for the separable inverse primary transformand a transform basis for the non-separable inverse primary transformcan be also expressed as a separable inverse primary transform basis anda non-separable inverse primary transform basis, respectively. Inaddition, their candidates can be also expressed as a separable inverseprimary transform basis candidate and a non-separable inverse primarytransform basis candidate.

Moreover, a transform basis for the separable inverse secondarytransform and a transform basis for the non-separable inverse secondarytransform can be also expressed as a separable inverse secondarytransform basis and a non-separable inverse secondary transform basis,respectively. In addition, their candidates can be also expressed as aseparable inverse secondary transform basis candidate and anon-separable inverse secondary transform basis candidate.

Here, the separable transform is a transform separable into directionaltransforms, for example, a transform separable into a vertical transformand a horizontal transform. The non-separable transform is a transforminseparable into directional transforms, for example, a transforminseparable into a vertical transform and a horizontal transform.

Similarly, the separable inverse transform is an inverse transformseparable into directional inverse transforms, for example, an inversetransform separable into a vertical inverse transform and a horizontalinverse transform. The non-separable inverse transform is an inversetransform inseparable into directional inverse transforms, for example,an inverse transform inseparable into a vertical inverse transform and ahorizontal inverse transform.

Moreover, for example, transformer 106 holds a table in which primarytransform basis candidates are associated with secondary transform basiscandidates. Transformer 106 selects, as a secondary transform basis, asecondary transform basis candidate associated with a primary transformbasis candidate selected as a primary transform basis, by reference tothe table.

Moreover, for example, inverse transformer 206 of decoder 200 holdscandidates and associations corresponding to the candidates andassociation held by transformer 106 of encoder 100. Inverse transformer206 of decoder 200 can determine an inverse primary transform basis andan inverse secondary transform basis in accordance with the candidatesand the association in the same manner as transformer 106 of encoder100.

Hereinafter, examples of an association between primary transform basiscandidates and secondary transform basis candidates will be described.It should be noted that, hereinafter, an expression such as DCT2 or DST7may mean a transform basis such as DCT2 or DST7.

FIG. 12 illustrates the first specific example of an association betweenseparable primary transform basis candidates and non-separable secondarytransform basis candidates. In this example, a primary transform is aseparable transform equivalent to only DCT2 and DST7, and a secondarytransform is a non-separable transform.

The example shows four primary transform basis candidates and foursecondary transform basis candidates. Specifically, the four primarytransform basis candidates include combinations of vertical DCT2 or DST7and horizontal DCT2 or DST7. The four secondary transform basiscandidates are transform bases 2 a, 2 b, 2 c, and 2 d. For example, eachof transform bases 2 a, 2 b, 2 c, and 2 d is a transform basisequivalent to the KL transform.

Transform basis 2 a is associated with the combination of vertical DCT2and horizontal DCT2. Transform basis 2 b is associated with thecombination of vertical DCT2 and horizontal DST7. Transform basis 2 c isassociated with the combination of vertical DST7 and horizontal DCT2.Transform basis 2 d is associated with the combination of vertical DST7and horizontal DST7.

Transformer 106 selects, as a secondary transform basis, a secondarytransform basis candidate associated with a primary transform basiscandidate selected as a primary transform basis. For example, whentransformer 106 selects the combination of vertical DST7 and horizontalDCT2 as a primary transform basis, transformer 106 selects transformbasis 2 c as a secondary transform basis.

Although the primary transform is equivalent to only DCT2 and DST7 inthe example, the primary transform may be equivalent to anothertransform. Moreover, although the four primary transform basiscandidates are used in the example, one primary transform basiscandidate may be used, two primary transform basis candidates may beused, three primary transform basis candidates may be used, or at leastfive primary transform basis candidates may be used.

Furthermore, although the primary transform is the separable transformand the second transform is the non-separable transform in the example,the primary transform is not limited to the separable transform and thesecondary transform is not limited to the non-separable transform.

In the example, the four secondary transform basis candidates are eachassociated with a corresponding one of the four primary transform basiscandidates, which are different. In other words, a secondary transformbasis candidate can be different for each primary transform basiscandidate. However, a secondary transform basis candidate need notalways be independent for each primary transform basis candidate. Forexample, one common secondary transform basis candidate may beassociated with at least two of the four primary transform basiscandidates, which are different.

Moreover, transform bases 2 b and 2 c are each associated with acorresponding one of the combination of vertical DCT2 and horizontalDST7 and the combination of vertical DST7 and horizontal DCT2. However,one common secondary transform basis candidate may be associated withprimary transform basis candidates constituting combinations of commontransform bases having only different direction attributes.

Moreover, two primary transform basis candidates for which the verticaldirection and the horizontal direction are interchanged as describedabove may be associated with two secondary transform basis candidatesone of which is obtained by transposing the other. For example, asecondary transform basis candidate is transposed by interchanging datapatterns constituting the secondary transform basis candidate. Morespecifically, the data patterns constituting the secondary transformbasis candidate constitute a matrix for the vertical direction and thehorizontal direction, and the secondary transform basis candidate may betransposed by transposing this matrix.

Moreover, one primary transform basis candidate may be associated withsecondary transform basis candidates. When transformer 106 selects, as aprimary transform basis, one primary transform basis candidateassociated with secondary transform basis candidates, transformer 106selects, as a secondary transform basis, one of the secondary transformbasis candidates associated with the one primary transform basiscandidate.

In this case, transformer 106 may select a secondary transform basisfrom among these secondary transform basis candidates, based on anevaluation value. Specifically, transformer 106 may calculate anevaluation value, such as a RD cost, for each of the secondary transformbasis candidates, and may select, as a secondary transform basis, thesecondary transform basis candidate having the best evaluation valuefrom among the secondary transform basis candidates. Alternatively,transformer 106 may select a secondary transform basis from among thesecondary transform basis candidates, based on any coding parameter,such as a block size or intra prediction mode.

Moreover, the number of at least one secondary transform basis candidateassociated with each primary transform basis candidate need not beconstant. In other words, when a primary transform basis candidatechanges, the number of the at least one secondary transform basiscandidate associated with the primary transform basis candidate mayvary. For example, the number of at least one secondary transform basiscandidate associated with the primary transform basis candidate may bedifferent for each primary transform basis candidate.

Moreover, when a primary transform basis candidate not associated with asecondary transform basis candidate in the table held by transformer 106etc. is selected, a predetermined transform basis may be selected.

FIG. 13 is a relationship diagram illustrating the second specificexample of an association between separable primary transform basiscandidates and non-separable secondary transform basis candidates. FIG.13 illustrates an example in which one common secondary transform basiscandidate is associated with at least two of primary transform basiscandidates. Specifically, in this example, transform basis 2 b isassociated with the combination of vertical DST7 and horizontal DCT2 andthe combination of vertical DST7 and horizontal DST7, compared to theexample illustrated in FIG. 12 .

In other words, transform basis 2 a is associated with the combinationof vertical DCT2 and horizontal DCT2, and transform basis 2 b isassociated with the other combinations. Only when transformer 106selects the combination of vertical DCT2 and horizontal DCT2 as aprimary transform basis, transformer 106 selects transform basis 2 a asa secondary transform basis; and in other cases, transformer 106 selectstransform basis 2 b as a secondary transform basis.

FIG. 14 is a relationship diagram illustrating the third specificexample of an association between separable primary transform basiscandidates and non-separable secondary transform basis candidates. Inthis example, no transform is associated with the combination ofvertical DST7 and horizontal DST7, compared to the example illustratedin FIG. 12 .

In other words, when transformer 106 selects the combination of verticalDST7 and horizontal DST7 as a primary transform basis, transformer 106performs no secondary transform (i.e., the secondary transform isskipped). In other cases, transformer 106 selects a secondary transformbasis based on a primary transform basis. Accordingly, transformer 106determines whether to perform the secondary transform, and the secondarytransform basis when the secondary transform is performed, based on theprimary transform basis.

It should be noted that, for example, performing no secondary transformis equivalent to performing no secondary transform that changes data.For this reason, performing no secondary transform includes formallyperforming a secondary transform that maintains data. A secondarytransform basis candidate of no transform may be a transform basis formaintaining data. Conversely, for example, performing a secondarytransform is equivalent to performing a secondary transform that changesdata.

FIG. 15 is a relationship diagram illustrating the fourth specificexample of an association between separable primary transform basiscandidates and non-separable secondary transform basis candidates. FIG.15 illustrates an example in which secondary transform basis candidatesare associated with one primary transform basis candidate.

Specifically, in this example, transform basis 2 e is further associatedwith the combination of vertical DCT2 and horizontal DCT2, compared tothe example illustrated in FIG. 12 . Moreover, transform basis 2 f isfurther associated with the combination of vertical DCT2 and horizontalDST7. Furthermore, transform basis 2 g is further associated with thecombination of vertical DST7 and horizontal DCT2.

In other words, at least one secondary transform basis candidate isassociated with one primary transform basis candidate. When transformer106 selects, as a primary transform basis, one primary transform basiscandidate associated with secondary transform basis candidates,transformer 106 selects, as a secondary transform basis, one of thesecondary transform basis candidates associated with the one primarytransform basis candidate.

In this case, transformer 106 may select a secondary transform basisfrom among these secondary transform basis candidates, based on anevaluation value, such as a RD cost. Alternatively, transformer 106 mayselect a secondary transform basis from among the secondary transformbasis candidates, based on any coding parameter, such as a block size orintra prediction mode.

For example, when transformer 106 selects the combination of verticalDCT2 and horizontal DCT2 as a primary transform basis, transformer 106selects transform basis 2 a or transform basis 2 e as a secondarytransform basis, based on an evaluation value or a coding parameter.

When transformer 106 selects, as a primary transform basis, one primarytransform basis candidate associated with one secondary transform basiscandidate, transformer 106 selects, as a secondary transform basis, theone secondary transform basis candidate associated with the one primarytransform basis candidate. In this example, when transformer 106 selectsthe combination of vertical DST7 and horizontal DST7 as a primarytransform basis, transformer 106 selects transform basis 2 d as asecondary transform basis.

Moreover, in the example, the one secondary transform basis candidate isassociated with the primary transform basis candidate corresponding tothe combination of vertical DST7 and horizontal DST7. Two secondarytransform basis candidates are associated with each of three otherprimary transform basis candidates. As in the example, the number of atleast one secondary transform basis candidate associated with eachprimary transform basis candidate need not be constant.

FIG. 16 is a relationship diagram illustrating the fifth specificexample of an association between separable primary transform basiscandidates and non-separable secondary transform basis candidates. Inthis example, no transform is used instead of transform basis 2 d andtransform basis 2 g, compared to the example illustrated in FIG. 15 .

In other words, at least one secondary transform basis candidate isassociated with one primary transform basis candidate. Further, the atleast one secondary transform basis candidate associated with the oneprimary transform basis candidate may include no transform.

For example, transform basis 2 c and no transform are associated withthe combination of vertical DST7 and horizontal DCT2. Stateddifferently, secondary transform basis candidates associated with theone primary transform basis candidate may include no transform.

When transformer 106 selects, as a primary transform basis, one primarytransform basis candidate associated with secondary transform basiscandidates including no transform, transformer 106 selects, as asecondary transform basis, one of the secondary transform basiscandidates. In this case, transformer 106 may select a secondarytransform basis from among these secondary transform basis candidates,based on an evaluation value, such as a RD cost. Alternatively,transformer 106 may select a secondary transform basis from among thesecondary transform basis candidates, based on any coding parameter,such as a block size or intra prediction mode.

When transformer 106 selects a secondary transform basis candidateincluding no transform as a secondary transform basis, transformer 106performs no secondary transform. On the other hand, when transformer 106selects another secondary transform basis candidate as the secondarytransform basis, transformer 106 performs the secondary transform usingthe selected secondary transform basis.

Specifically, when transformer 106 selects the combination of verticalDST7 and horizontal DCT2 as a primary transform basis, transformer 106selects transform basis 2 c or no transform as a secondary transformbasis. Then, when transformer 106 selects transform basis 2 c as thesecondary transform basis, transformer 106 performs the secondarytransform using transform basis 2 c. On the other hand, when transformer106 selects no transform as the secondary transform basis, transformer106 performs no secondary transform (i.e., the secondary transform isskipped).

In this example, at least one secondary transform basis candidateincluding no transform is determined for each primary transform basiscandidate. Specifically, at least one secondary transform basiscandidate including no transform is different for each primary transformbasis candidate. Accordingly, whether to perform the secondary transformand a secondary transform basis when the secondary transform isperformed are determined depending on the primary transform basis.

FIG. 17 is a relationship diagram illustrating the first specificexample of an association between separable primary transform basiscandidates and separable secondary transform basis candidates. In thisexample, a primary transform is a separable transform corresponding toonly DCT2 and DST7, and a secondary transform is a separable transform.The example shows four primary transform basis candidates and foursecondary transform basis candidates. The four primary transform basiscandidates are the same as those in the example illustrated in FIG. 12 .

The four secondary transform basis candidates are the combination ofvertical transform basis 2 a 1 and horizontal transform basis 2 a 2, thecombination of vertical transform basis 2 b 1 and horizontal transformbasis 2 b 2, the combination of vertical transform basis 2 c 1 andhorizontal transform basis 2 c 2, and the combination of verticaltransform basis 2 d 1 and horizontal transform basis 2 d 2.

The combination of vertical transform basis 2 a 1 and horizontaltransform basis 2 a 2 is associated with the combination of verticalDCT2 and horizontal DCT2. The combination of vertical transform basis 2b 1 and horizontal transform basis 2 b 2 is associated with thecombination of vertical DCT2 and horizontal DST7.

The combination of vertical transform basis 2 c 1 and horizontaltransform basis 2 c 2 is associated with the combination of verticalDST7 and horizontal DCT2. The combination of vertical transform basis 2d 1 and horizontal transform basis 2 d 2 is associated with thecombination of vertical DST7 and horizontal DST7.

Transformer 106 selects, as a secondary transform basis, a secondarytransform basis candidate associated with a primary transform basiscandidate selected as a primary transform basis. For example, whentransformer 106 selects the combination of vertical DST7 and horizontalDCT2 as a primary transform basis, transformer 106 selects thecombination of vertical transform basis 2 c 1 and horizontal transformbasis 2 c 2 as a secondary transform basis.

Although the primary transform is equivalent to only DCT2 and DST7 inthe example, the primary transform may be equivalent to anothertransform. Moreover, although the four primary transform basiscandidates are used in the example, one primary transform basiscandidate may be used, two primary transform basis candidates may beused, three primary transform basis candidates may be used, or at leastfive primary transform basis candidates may be used.

In the example, the combinations of the vertical transform bases and thehorizontal transform bases are used as the secondary transform basiscandidates, and each of the vertical transform bases and the horizontaltransform bases is determined independently. In other words, thevertical transform basis and the horizontal transform basis can bedifferent. However, the vertical transform basis and the horizontaltransform basis need not be independent of each other. Stateddifferently, the vertical transform basis and the horizontal transformbasis may be set as one common transform basis for the verticaldirection and the horizontal direction.

Furthermore, in the example, the four secondary transform basiscandidates are each associated with a corresponding one of the fourprimary transform basis candidates, which are different. In other words,a secondary transform basis candidate can be different for each primarytransform basis candidate. However, a secondary transform basiscandidate need not always be independent for each primary transformbasis candidate. For example, one common secondary transform basiscandidate may be associated with at least two of the four primarytransform basis candidates, which are different.

Specifically, the combination of vertical transform basis 2 a 1 andhorizontal transform basis 2 a 2 may be associated with the combinationof vertical DCT2 and horizontal DCT2. The combination of verticaltransform basis 2 b 1 and horizontal transform basis 2 b 2 may beassociated with the other combinations.

Moreover, in the example, the secondary transform basis candidateassociated with the combination of vertical DCT2 and horizontal DST7 isdifferent from the secondary transform basis candidate associated withthe combination of vertical DST7 and horizontal DCT2. However, onecommon secondary transform basis candidate may be associated withprimary transform basis candidates constituting combinations of commontransform bases having only different direction attributes.

Moreover, two primary transform basis candidates for which the verticaldirection and the horizontal direction are interchanged as describedabove may be associated with two secondary transform basis candidatesone of which is obtained by transposing the other. For example, asecondary transform basis candidate is transposed by interchanging datapatterns constituting the secondary transform basis candidate. Morespecifically, the data patterns constituting the secondary transformbasis candidate form a matrix, and the secondary transform basiscandidate may be transposed by transposing this matrix.

Furthermore, in transposing a secondary transform basis candidateincluding a vertical transform basis and a horizontal transform basis,the vertical transform basis and the horizontal transform basis may beeach transposed. Alternatively, the vertical transform basis and thehorizontal transform basis may be transposed by being interchanged witheach other. Alternatively, the vertical transform basis and thehorizontal transform basis may be each transposed and interchanged witheach other.

Moreover, one primary transform basis candidate may be associated withsecondary transform basis candidates. When transformer 106 selects, as aprimary transform basis, one primary transform basis candidateassociated with secondary transform basis candidates, transformer 106selects, as a secondary transform basis, one of the secondary transformbasis candidates associated with the one primary transform basiscandidate.

In this case, transformer 106 may select a secondary transform basisfrom among these secondary transform basis candidates, based on anevaluation value, such as a RD cost. Alternatively, transformer 106 mayselect a secondary transform basis from among the secondary transformbasis candidates, based on any coding parameter, such as a block size orintra prediction mode.

Moreover, the number of at least one secondary transform basis candidateassociated with each primary transform basis candidate need not beconstant. In other words, when a primary transform basis candidatechanges, the number of the at least one secondary transform basiscandidate associated with the primary transform basis candidate mayvary. For example, the number of at least one secondary transform basiscandidate associated with the primary transform basis candidate may bedifferent for each primary transform basis candidate.

Moreover, when a primary transform basis candidate not associated with asecondary transform basis candidate in the table held by transformer 106etc. is selected, a predetermined transform basis may be selected.

Although FIG. 13 to FIG. 16 illustrate the variations of the exampleillustrated in FIG. 12 , variations similar to the variations of FIG. 13to FIG. 16 can be applied to the example illustrated in FIG. 17 .

For example, as illustrated in FIG. 13 , one common secondary transformbasis candidate may be associated with primary transform basiscandidates. As illustrated in FIG. 14 , no transform may be associatedas a secondary transform basis candidate with a primary transform basiscandidate. As illustrated in FIG. 15 , at least one secondary transformbasis candidate may be associated with one primary transform basiscandidate. As illustrated in FIG. 16 , secondary transform basiscandidates including no transform may be associated with one primarytransform basis candidate.

FIG. 18 is a relationship diagram illustrating the second specificexample of an association between separable primary transform basiscandidates and separable secondary transform basis candidates. FIG. 18illustrates an example in which a vertical transform basis and ahorizontal transform basis are set as one common transform basis for thevertical direction and the horizontal direction. Specifically, in thisexample, two transform bases constituting a combination used as asecondary transform basis candidate are set as one common transformbasis for the vertical direction and the horizontal direction, comparedto the example illustrated in FIG. 17 .

In other words, for a secondary transform basis candidate that is acombination of a vertical transform basis and a horizontal transformbasis, the horizontal transform basis is identical to the verticaltransform basis. For example, for the secondary transform basiscandidate associated with the combination of vertical DCT2 andhorizontal DCT2, horizontal transform basis 2 a 1 is identical tovertical transform basis 2 a 1. This standardizes and simplifiesprocessing.

Moreover, in the example, for all the secondary transform basiscandidates, the vertical transform bases are identical to the horizontaltransform bases. However, for part of the secondary transform basiscandidates, the vertical transform bases may be identical to thehorizontal transform bases. Stated differently, the secondary transformbasis candidates may include a transform basis candidate for which avertical transform basis is identical to a horizontal transform basis,and a transform basis candidate for which a vertical transform basis isdifferent from a horizontal transform basis.

When one primary transform basis candidate is associated with secondarytransform basis candidates, for all the second transform basiscandidates associated with the one primary transform basis candidate,vertical transform bases may be identical to horizontal transform bases.Alternatively, for part of the secondary transform basis candidatesassociated with the one primary transform basis candidate, the verticaltransform bases may be identical to the horizontal transform bases.

FIG. 19 is a relationship diagram illustrating a specific example of anassociation between non-separable primary transform basis candidates andnon-separable secondary transform basis candidates. In this example,each of a primary transform and a secondary transform is a non-separabletransform.

The example shows four primary transform basis candidates and foursecondary transform basis candidates. The four secondary transform basiscandidates are transform bases 1 a, 1 b, 1 c, and 1 d. The foursecondary transform basis candidates are transform bases 2 a, 2 b, 2 c,and 2 d. For example, each of the four primary transform basiscandidates and the four secondary transform basis candidates isequivalent to the KL transform. Transform bases 1 a, 1 b, 1 c, and 1 dare associated with transform bases 2 a, 2 b, 2 c, and 2 d,respectively.

Transformer 106 selects, as a secondary transform basis, a secondarytransform basis candidate associated with a primary transform basiscandidate selected as a primary transform basis. For example, whentransformer 106 selects transform basis 1 c as a primary transformbasis, transformer 106 selects transform basis 2 c as a secondarytransform basis.

Moreover, although the four primary transform basis candidates are usedin the example, one primary transform basis candidate may be used, twoprimary transform basis candidates may be used, three primary transformbasis candidates may be used, or at least five primary transform basiscandidates may be used.

Furthermore, in the example, the four secondary transform basiscandidates are each associated with a corresponding one of the fourprimary transform basis candidates, which are different. In other words,a secondary transform basis candidate can be different for each primarytransform basis candidate. However, a secondary transform basiscandidate need not always be independent for each primary transformbasis candidate. For example, one common secondary transform basiscandidate may be associated with at least two of the four primarytransform basis candidates, which are different.

Specifically, transform basis 2 a may be associated with transform basis1 a, and transform basis 2 b may be associated with each of transformbases 1 b, 1 c, and 1 d.

Moreover, secondary transform basis candidates may be associated withone primary transform basis candidate. When transformer 106 selects, asa primary transform basis, one primary transform basis candidateassociated with secondary transform basis candidates, transformer 106selects, as a secondary transform basis, one of the secondary transformbasis candidates associated with the one primary transform basiscandidate.

In this case, transformer 106 may select a secondary transform basisfrom among these secondary transform basis candidates, based on anevaluation value, such as a RD cost. Alternatively, transformer 106 mayselect a secondary transform basis from among the secondary transformbasis candidates, based on any coding parameter, such as a block size orintra prediction mode.

Moreover, the number of at least one secondary transform basis candidateassociated with each primary transform basis candidate need not beconstant. In other words, when a primary transform basis candidatechanges, the number of the at least one secondary transform basiscandidate associated with the primary transform basis candidate mayvary. For example, the number of at least one secondary transform basiscandidate associated with the primary transform basis candidate may bedifferent for each primary transform basis candidate.

Moreover, when a primary transform basis candidate not associated with asecondary transform basis candidate in the table held by transformer 106etc. is selected, a predetermined transform basis may be selected.

Although FIG. 13 to FIG. 16 illustrate the variations of the exampleillustrated in FIG. 12 , variations similar to the variations of FIG. 13to FIG. 16 can be applied to the example illustrated in FIG. 19 .

For example, as illustrated in FIG. 13 , one common secondary transformbasis candidate may be associated with primary transform basiscandidates. As illustrated in FIG. 14 , no transform may be associatedas a secondary transform basis candidate with a primary transform basiscandidate. As illustrated in FIG. 15 , at least one secondary transformbasis candidate may be associated with one primary transform basiscandidate. As illustrated in FIG. 16 , secondary transform basiscandidates including no transform may be associated with one primarytransform basis candidate.

FIG. 20 is a relationship diagram illustrating a specific example of anassociation between non-separable primary transform basis candidates andseparable secondary transform basis candidates. In this example, aprimary transform is a non-separable transform, and a secondarytransform is a separable transform. The example shows four primarytransform basis candidates and four secondary transform basiscandidates.

The four secondary transform basis candidates are transform bases 1 a, 1b, 1 c, and 1 d. The four secondary transform basis candidates are thecombination of vertical transform basis 2 a 1 and horizontal transformbasis 2 a 2, the combination of vertical transform basis 2 b 1 andhorizontal transform basis 2 b 2, the combination of vertical transformbasis 2 c 1 and horizontal transform basis 2 c 2, and the combination ofvertical transform basis 2 d 1 and horizontal transform basis 2 d 2. Forexample, each of the four primary transform basis candidates and thefour secondary transform basis candidates is equivalent to the KLtransform.

The combination of vertical transform basis 2 a 1 and horizontaltransform basis 2 a 2 is associated with transform basis 1 a. Thecombination of vertical transform basis 2 b 1 and horizontal transformbasis 2 b 2 is associated with transform basis 1 b. The combination ofvertical transform basis 2 c 1 and horizontal transform basis 2 c 2 isassociated with transform basis 1 c. The combination of verticaltransform basis 2 d 1 and horizontal transform basis 2 d 2 is associatedwith transform basis 1 d.

Transformer 106 selects, as a secondary transform basis, a secondarytransform basis candidate associated with a primary transform basiscandidate selected as a primary transform basis. For example, whentransformer 106 selects transform basis 1 c as a primary transformbasis, transformer 106 selects the combination of vertical transformbasis 2 c 1 and horizontal transform basis 2 c 2 as a secondarytransform basis.

Although the four primary transform basis candidates are used in theexample, one primary transform basis candidate may be used, two primarytransform basis candidates may be used, three primary transform basiscandidates may be used, or at least five primary transform basiscandidates may be used.

In the example, the combinations of the vertical transform bases and thehorizontal transform bases are used as the secondary transform basiscandidates, and each of the vertical transform bases and the horizontaltransform bases is determined independently. In other words, thevertical transform basis and the horizontal transform basis can bedifferent. However, the vertical transform basis and the horizontaltransform basis need not be independent of each other. Stateddifferently, the vertical transform basis and the horizontal transformbasis may be set as one common transform basis for the verticaldirection and the horizontal direction.

Furthermore, in the example, the four secondary transform basiscandidates are each associated with a corresponding one of the fourprimary transform basis candidates, which are different. In other words,a secondary transform basis candidate can be different for each primarytransform basis candidate. However, a secondary transform basiscandidate need not always be independent for each primary transformbasis candidate. For example, one common secondary transform basiscandidate may be associated with at least two of the four primarytransform basis candidates, which are different.

Specifically, the combination of vertical transform basis 2 a 1 andhorizontal transform basis 2 a 2 may be associated with transform basis1 a. The combination of vertical transform basis 2 b 1 and horizontaltransform basis 2 b 2 may be associated with each of transform bases 1b, 1 c, and 1 d.

Moreover, secondary transform basis candidates may be associated withone primary transform basis candidate. When transformer 106 selects, asa primary transform basis, one primary transform basis candidateassociated with secondary transform basis candidates, transformer 106selects, as a secondary transform basis, one of the secondary transformbasis candidates associated with the one primary transform basiscandidate.

In this case, transformer 106 may select a secondary transform basisfrom among these secondary transform basis candidates, based on anevaluation value, such as a RD cost. Alternatively, transformer 106 mayselect a secondary transform basis from among the secondary transformbasis candidates, based on any coding parameter, such as a block size orintra prediction mode.

Moreover, the number of at least one secondary transform basis candidateassociated with each primary transform basis candidate need not beconstant. In other words, when a primary transform basis candidatechanges, the number of the at least one secondary transform basiscandidate associated with the primary transform basis candidate mayvary. For example, the number of at least one secondary transform basiscandidate associated with the primary transform basis candidate may bedifferent for each primary transform basis candidate.

Moreover, when a primary transform basis candidate not associated with asecondary transform basis candidate in the table held by transformer 106etc. is selected, a predetermined transform basis may be selected.

Although FIG. 13 to FIG. 16 illustrate the variations of the exampleillustrated in FIG. 12 , variations similar to the variations of FIG. 13to FIG. 16 can be applied to the example illustrated in FIG. 20 .

For example, as illustrated in FIG. 13 , one common secondary transformbasis candidate may be associated with primary transform basiscandidates. As illustrated in FIG. 14 , no transform may be associatedas a secondary transform basis candidate with a primary transform basiscandidate. As illustrated in FIG. 15 , at least one secondary transformbasis candidate may be associated with one primary transform basiscandidate. As illustrated in FIG. 16 , secondary transform basiscandidates including no transform may be associated with one primarytransform basis candidate.

Although FIG. 18 illustrates the variation of the example illustrated inFIG. 17 , a variation similar to the variation of FIG. 18 can be appliedto the example illustrated in FIG. 20 . For example, as illustrated inFIG. 18 , a common transform basis for the vertical direction and thehorizontal direction may be used as a secondary transform basis.

FIG. 21 is a relationship diagram illustrating a specific example of anassociation between primary transform basis candidates and secondarytransform basis candidates in a state in which separable transforms andnon-separable transforms are present.

Primary transform basis candidates may include a separable primarytransform basis candidate, or may include a non-separable primarytransform basis candidate. Transformer 106 performs a separable primarytransform or a non-separable primary transform according to a primarytransform basis candidate selected as a primary transform basis.

In other words, when transformer 106 selects a separable primarytransform basis candidate as a primary transform basis, transformer 106performs the separable primary transform using the separable primarytransform basis candidate selected as the primary transform basis. Whentransformer 106 selects a non-separable primary transform basiscandidate as the primary transform basis, transformer 106 performs thenon-separable primary transform using the non-separable primarytransform basis candidate selected as the primary transform basis.

A separable secondary transform basis candidate may be associated with aseparable primary transform basis candidate, a non-separable secondarytransform basis candidate may be associated with the separable primarytransform basis candidate, or both of them may be associated with theseparable primary transform basis candidate. Further, a separablesecondary transform basis candidate may be associated with anon-separable primary transform basis candidate, a non-separablesecondary transform basis candidate may be associated with thenon-separable primary transform basis candidate, or both of them may beassociated with the non-separable primary transform basis candidate.Transformer 106 performs a separable secondary transform or anon-separable secondary transform according to a secondary transformbasis candidate selected as a secondary transform basis.

In other words, when transformer 106 selects the separable secondarytransform basis candidate as the secondary transform basis, transformer106 performs the separable secondary transform using the separablesecondary transform basis candidate selected as the secondary transformbasis. Moreover, when transformer 106 selects the non-separablesecondary transform basis candidate as the secondary transform basis,transformer 106 performs the non-separable secondary transform using thenon-separable secondary transform basis candidate selected as thesecondary transform basis.

Although the secondary transform basis is selected based on the primarytransform basis in the above description, the secondary transform basismay be selected based on the primary transform basis and a codingparameter. A coding parameter is encoded by encoder 100 and is decodedby decoder 200. In the following description, an intra prediction modeis used as a coding parameter for selecting a secondary transform basis.

FIG. 22 is a flow chart illustrating selection of a secondary transformbasis based on a primary transform basis and an intra prediction mode.For example, transformer 106 of encoder 100 illustrated in FIG. 1performs the selection illustrated in FIG. 22 .

The selection of the primary transform basis (S201) illustrated in FIG.22 is the same as the selection of the primary transform basis (S101)illustrated in FIG. 11 . In the selection of the secondary transformbasis (S202) illustrated in FIG. 22 , transformer 106 selects asecondary transform basis associated with a primary transform basis andan intra prediction mode, compared to the selection of the secondarytransform basis (S102) illustrated in FIG. 11 .

In other words, in the example illustrated in FIG. 22 , the intraprediction mode is used in addition to the primary transform basis. Theintra prediction mode includes, for example, an intra predictiondirection and a luminance and chrominance prediction mode (LMChromamode). For example, when the selected primary transform basiscorresponds to a combination of vertical DCT2 and horizontal DCT2, andthe intra prediction mode is a planar prediction, transformer 106selects a secondary transform basis candidate associated with thecombination of vertical DCT2 and horizontal DCT2 and the planarprediction.

The secondary transform basis candidate associated with the combinationof vertical DCT2 and horizontal DCT2 and the planar prediction may be asecondary transform basis candidate updated by offline learning usingtraining data corresponding to coefficient information in the case ofthe combination of vertical DCT2 and horizontal DCT2 and the planarprediction. Alternatively, a secondary transform basis candidateequivalent to the KL transform may be determined using a coefficientinformation model obtained from the combination of vertical DCT2 andhorizontal DCT2, based on a prediction error model derived based on theGauss-Markov model regarding the planar prediction.

FIG. 23 is a relationship diagram illustrating a specific example of anassociation between intra prediction modes, separable primary transformbasis candidates, and non-separable secondary transform basiscandidates. In this example, planar prediction and DC prediction areindicated as an intra prediction mode. Further, other intra predictionmodes may be used. A primary transform is a separable transformequivalent to only DCT2 and DST7, and a secondary transform is anon-separable transform.

Moreover, in the example, primary transform basis candidates are thecombination of vertical DCT2 and horizontal DCT2, the combination ofvertical DCT2 and horizontal DST7, the combination of vertical DST7 andhorizontal DCT2, the combination of vertical DST7 and horizontal DST7,etc. Secondary transform basis candidates are transform bases 2 a, 2 b,2 c, 2 d, 2 e, 2 f, 2 g, and 2 h etc. For example, each of the secondarytransform basis candidates is equivalent to the KL transform.

Transform basis 2 a is associated with the planar prediction and thecombination of vertical DCT2 and horizontal DCT2. Transform basis 2 b isassociated with the planar prediction and the combination of verticalDCT2 and horizontal DST7. Transform basis 2 c is associated with theplanar prediction and the combination of vertical DST7 and horizontalDCT2. Transform basis 2 d is associated with the planar prediction andthe combination of vertical DST7 and horizontal DST7.

Transform basis 2 e is associated with the DC prediction and thecombination of vertical DCT2 and horizontal DCT2. Transform basis 2 f isassociated with the DC prediction and the combination of vertical DCT2and horizontal DST7. Transform basis 2 g is associated with the DCprediction and the combination of vertical DST7 and horizontal DCT2.Transform basis 2 h is associated with the DC prediction and thecombination of vertical DST7 and horizontal DST7.

Transformer 106 selects, as a secondary transform basis, a secondarytransform basis candidate associated with the intra prediction mode usedfor prediction and a primary transform basis candidate selected as aprimary transform basis. For example, when the DC prediction is used asthe intra prediction mode, and transformer 106 selects the combinationof vertical DST7 and horizontal DCT2 as a primary transform basis,transformer 106 selects transform basis 2 g as a secondary transformbasis.

In the example, primary transform basis candidates are associated withsecondary transform basis candidates for each intra prediction mode. Inother words, an association between the primary transform basiscandidates and the secondary transform basis candidates can be differentfor each intra prediction mode. Transformer 106 refers to a table asillustrated in FIG. 23 , and selects a secondary transform basiscandidate associated with an intra prediction mode and a primarytransform basis, based on the intra prediction mode and the primarytransform basis.

However, the association between the primary transform basis candidatesand the secondary transform basis candidates need not always bedifferent for each intra prediction mode. For example, an associationbetween primary transform basis candidates and secondary transform basiscandidates may be common to at least two of different intra predictionmodes.

The primary transform basis candidates and the secondary transform basiscandidates associated with each other for each intra prediction modehave the same relationship as the relationship illustrated in FIG. 12 .Stated differently, the description of the example illustrated in FIG.12 can be applied to the example illustrated in FIG. 23 . In addition,the variations illustrated in FIG. 13 to FIG. 21 can be applied to theprimary transform basis candidates and the secondary transform basiscandidates associated with each other for each intra prediction mode.

For example, as illustrated in FIG. 13 , one common secondary transformbasis candidate may be associated with primary transform basiscandidates. As illustrated in FIG. 14 , no transform may be associatedas a secondary transform basis candidate with a primary transform basiscandidate. As illustrated in FIG. 15 , at least one secondary transformbasis candidate may be associated with one primary transform basiscandidate. As illustrated in FIG. 16 , secondary transform basiscandidates including no transform may be associated with one primarytransform basis candidate.

As illustrated in FIG. 17 , each of the primary transform and thesecondary transform may be a separable transform. As illustrated in FIG.18 , a vertical transform basis and a horizontal transform basis may beidentical in a separable secondary transform basis candidate. Asillustrated in FIG. 19 , each of the primary transform and the secondarytransform may be a non-separable transform. As illustrated in FIG. 20 ,the primary transform may be a non-separable transform, and thesecondary transform may be a separable transform. As illustrated in FIG.21 , each of the primary transform and the secondary transform mayinclude a separable transform and a non-separable transform.

Although the intra prediction mode is used as the coding parameter forselecting the secondary transform basis in the above description, thecoding parameter for selecting the secondary transform basis is notlimited to the intra prediction mode. At least one of parameters, suchas block sizes, quantization parameters, motion vector lengths of motionvectors, or directions of motion vectors, can be used as the codingparameter for selecting the secondary transform basis. In other words,at least one of these may be associated with a primary transform basiscandidate and a secondary transform basis candidate.

Moreover, for example, the above coding parameter may be a parameterdifferent from a parameter relating to a transform, and a parameterrelating to splitting corresponding to a block size etc., predictioncorresponding to a picture type etc., quantization, or filter.

In selection of a secondary transform basis based on a primary transformbasis and a coding parameter, there is a possibility that processing iscomplex and the amount of processing is large, compared to selection ofa secondary transform basis based on only the primary transform basis.However, the selection of the secondary transform basis based on theprimary transform basis and the coding parameter results in appropriateselection of the secondary transform basis. Accordingly, it is possibleto further reduce a coding amount.

Regarding the selection of the secondary transform basis described usingFIG. 11 to FIG. 23 , when a secondary transform basis is uniquelydetermined based on not an evaluation value but on a primary transformbasis or a primary transform basis and a coding parameter, informationindicating the secondary transform basis need not be encoded. In thiscase, the information indicating the secondary transform basis need notbe decoded.

Similarly, when a primary transform basis is uniquely determined basedon not an evaluation value but on a coding parameter, informationindicating the primary transform basis need not be encoded. In thiscase, the information indicating the primary transform basis need not bedecoded. When a primary transform basis is uniquely determined based onnot an evaluation value but on a secondary transform basis or asecondary transform basis and a coding parameter, information indicatingthe secondary transform basis is encoded, and information indicating theprimary transform basis need not be encoded. In this case, theinformation indicating the primary transform basis need not be decoded.

Accordingly, encoder 100 may encode only one of the primary transformbasis and the secondary transform basis. Decoder 200 may decode only oneof the primary transform basis and the secondary transform basis.

The bit count of the information indicating the secondary transformbasis may depend on the number of at least one secondary transform basiscandidate associated with a selected primary transform basis candidateetc. For example, when the number of at least one secondary transformbasis candidate associated with a selected primary transform basiscandidate etc. is two, the secondary transform basis may be indicated by1 bit. In other words, in this case, a 1-bit syntax element may beencoded and decoded as information indicating the secondary transformbasis. Similarly, the bit count of the information indicating theprimary transform basis may depend on the number of primary transformbasis candidates.

The number of the at least one secondary transform basis candidateassociated with the primary transform basis candidate etc. may beadaptively determined according to the primary transform basiscandidate, the intra prediction mode, the block size, etc. For example,when a primary transform basis candidate is a combination of verticalDCT2 and horizontal DCT2, and the intra prediction mode is the planarprediction or the DC prediction, two secondary transform basiscandidates may be used; and in other cases, three secondary transformbasis candidates may be used.

Although the secondary transform basis is selected based on the primarytransform basis etc. in the above description, when a secondarytransform basis is selected before a primary transform basis, theprimary transform basis may be selected based on the selected secondarytransform basis etc. For example, transformer 106 may select a primarytransform basis associated with a selected secondary transform basisetc.

Similarly, although the inverse secondary transform basis is selectedbased on the inverse primary transform basis etc. in the abovedescription, when an inverse secondary transform basis is selectedbefore an inverse primary transform basis, the inverse primary transformbasis may be selected based on the selected inverse secondary transformbasis etc. For example, transformer 206 may select an inverse primarytransform basis associated with a selected inverse secondary transformbasis etc.

Transformer 106 may perform a secondary transform not entirely butpartially on the result of a primary transform. For example, transformer106 may perform the secondary transform on low frequency components ofthe result of the primary transform, or may not perform the secondarytransform on high frequency components of the result of the primarytransform. In other words, transformer 106 may perform the secondarytransform on a sub-block having an arbitrary size in the low frequencyside in a block to be transformed.

A transform matrix may not always be used in each of the primarytransform and the secondary transform. For example, a transform functionequivalent to a transform matrix may be used. An orthogonal transformequivalent to the primary transform or the secondary transform may beperformed by superimposing Givens rotations. Butterfly computation maybe used.

For example, a separable transform and a non-separable transform may bepresent in the primary transform or the secondary transform. Forexample, when the intra prediction mode indicates 18 equivalent to ahorizontal intra prediction direction, 50 equivalent to a vertical intraprediction direction, or a value close to these, the separable transformmay be used. In other cases, the non-separable transform may be used. Inother words, a separable transform basis or a non-separable transformbasis may be selected based on the intra prediction mode.

The selection of the secondary transform basis based on the primarytransform basis etc. may be enabled or disabled on a per slice basis. Inother words, information indicating whether the selection of thesecondary transform basis based on the primary transform basis etc. isenabled may be encoded and decoded for each slice. Moreover, theselection of the secondary transform basis based on the primarytransform basis etc. may be enabled or disabled on a per tile basis. Inother words, information indicating whether the selection of thesecondary transform basis based on the primary transform basis etc. isenabled may be encoded and decoded for each tile.

Furthermore, the selection of the secondary transform basis based on theprimary transform basis etc. may be enabled or disabled on a per CTUbasis. In other words, information indicating whether the selection ofthe secondary transform basis based on the primary transform basis etc.is enabled may be encoded and decoded for each CTU. Moreover, theselection of the secondary transform basis based on the primarytransform basis etc. may be enabled or disabled on a per CU basis. Inother words, information indicating whether the selection of thesecondary transform basis based on the primary transform basis etc. isenabled may be encoded and decoded for each CU.

Furthermore, the selection of the secondary transform basis based on theprimary transform basis etc. may be enabled or disabled according to aframe type such as an I frame, a P frame, or a B frame. Moreover, theselection of the secondary transform basis based on the primarytransform basis etc. may be enabled or disabled according to aprediction mode such as the intra prediction or the inter prediction.

Furthermore, the selection of the secondary transform basis based on theprimary transform basis etc. may be enabled or disabled according toluminance or chrominance. For example, the selection of the secondarytransform basis based on the primary transform basis etc. may beperformed for one of the luminance and the chrominance, and theselection of the secondary transform basis based on the primarytransform basis etc. may not be performed for the other of the luminanceand the chrominance. Alternatively, the selection of the secondarytransform basis based on the primary transform basis etc. may beperformed for each of the luminance and the chrominance.

When transformer 106 does not perform the selection of the secondarytransform basis based on the primary transform basis etc., transformer106 may select a secondary transform basis based on another selectioncriterion. For example, transformer 106 may select a predeterminedsecondary transform basis, may select a secondary transform basis basedon an evaluation value, or may select a secondary transform basis basedon a coding parameter.

Transformer 106 is not limited to selecting a primary transform basisfrom among primary transform basis candidates, or may determine aprimary transform basis more flexibly. For example, transformer 106 mayconstruct a primary transform basis dynamically according to a codingparameter etc., or may adjust a selected primary transform basisaccording to a coding parameter etc.

Similarly, transformer 106 is not limited to selecting a secondarytransform basis from among secondary transform basis candidates, or maydetermine a secondary transform basis more flexibly. For example, indetermining a secondary transform basis, transformer 106 may generatethe secondary transform basis dynamically according to a primarytransform basis etc., or may adjust a selected secondary transform basisaccording to a coding parameter etc.

[Implementation Example of Encoder]

FIG. 24 is a block diagram illustrating an implementation example ofencoder 100 according to Embodiment 1. Encoder 100 includes processor160 and memory 162. For example, the plurality of constituent elementsof encoder 100 illustrated in FIG. 1 are implemented by processor 160and memory 162 illustrated in FIG. 24 .

Processor 160 is an electronic circuit accessible to memory 162, andperforms information processing. For example, processor 160 is anexclusive or general processor that encodes a video using memory 162.Processor 160 may be a central processing unit (CPU).

Processor 160 may include a plurality of electronic circuits, or mayinclude a plurality of sub-processors. Moreover, processor 160 mayperform the functions of constituent elements among the plurality ofconstituent elements of encoder 100 illustrated in FIG. 1 , except theconstituent elements that store information.

Memory 162 is an exclusive or general memory for storing informationused by processor 160 to encode a video. Memory 162 may be an electroniccircuit, may be connected to processor 160, or may be included inprocessor 160.

Memory 162 may include a plurality of electronic circuits, or mayinclude a plurality of sub-memories. Memory 162 may be a magnetic diskor an optical disc etc., or may be expressed as storage or a recordingmedium etc. Further, memory 162 may be a non-volatile memory or avolatile memory.

Moreover, memory 162 may perform the functions of, among the pluralityof constituent elements of encoder 100 illustrated in FIG. 1 , theconstituent elements that store information. Specifically, memory 162may perform the functions of block memory 118 and frame memory 122illustrated in FIG. 1 .

Memory 162 may store a video to be encoded, or may store a bitstreamcorresponding to an encoded video. Moreover, memory 162 may store aprogram for causing processor 160 to encode a video. Furthermore, memory162 may store information etc. indicating an association between primarytransform basis candidates and secondary transform basis candidates.

It should be noted that not all of the plurality of constituent elementsillustrated in FIG. 1 need to be implemented by encoder 100, and not allof the processes described above need to be performed by encoder 100.Some of the plurality of constituent elements illustrated in FIG. 1 maybe included in another device, and some of the processes described abovemay be performed by another device. Processing relating to transform isproperly performed by encoder 100 implementing some of the plurality ofconstituent elements illustrated in FIG. 1 and performing some of theprocesses described above.

FIG. 25 is a flow chart illustrating an example of operations performedby encoder 100 illustrated in FIG. 24 . For example, encoder 100illustrated in FIG. 24 performs the operations illustrated in FIG. 25when encoder 100 encodes a video.

Specifically, processor 160 derives a prediction error by subtracting aprediction image from an image included in a video (S301). Next,processor 160 determines a secondary transform basis based on a primarytransform basis (S302). Then, processor 160 performs a primary transformon the prediction error using the primary transform basis (S303). Next,processor 160 performs a secondary transform on the result of theprimary transform using the secondary transform basis (S304).

After that, processor 160 performs quantization on the result of thesecondary transform (S305). Finally, processor 160 encodes a result ofthe quantization as data of the image (S306).

For example, processor 160 may determine the secondary transform basisbased on the primary transform basis and a parameter encoded when theprocessor encodes the video. This parameter may be a parameterindicating an intra prediction mode. In addition, processor 160 maydetermine the secondary transform basis based on the primary transformbasis and the intra prediction mode indicated by the parameter.

Moreover, for example, processor 160 may determine the primary transformbasis from among a plurality of primary transform basis candidates. Inaddition, processor 160 may determine the secondary transform basis fromamong at least one secondary transform basis candidate associated with aprimary transform basis candidate determined as the primary transformbasis among the plurality of primary transform basis candidates.

Moreover, for example, at least two of the plurality of primarytransform basis candidates may be associated with a common secondarytransform basis candidate. Furthermore, a total number of at least onesecondary transform basis candidate associated with the primarytransform basis candidate may depend on the primary transform basiscandidate.

Moreover, for example, the secondary transform basis determined when theprimary transform basis is a combination of a first transform basis fora vertical direction and a second transform basis for a horizontaldirection may be identical to the secondary transform basis determinedwhen the primary transform basis is a combination of the secondtransform basis for the vertical direction and the first transform basisfor the horizontal direction. Furthermore, the secondary transform basisdetermined when the primary transform basis is a combination of a firsttransform basis for a vertical direction and a second transform basisfor a horizontal direction may be a transform basis obtained bytransposing the secondary transform basis determined when the primarytransform basis is a combination of the second transform basis for thevertical direction and the first transform basis for the horizontaldirection.

Moreover, for example, when the secondary transform basis is acombination of a transform basis for a vertical direction and atransform basis for a horizontal direction, the transform basis for thevertical direction and the transform basis for the horizontal directionmay be identical.

Moreover, for example, processor 160 may encode only one of theinformation indicating the primary transform basis and the informationindicating the secondary transform basis.

Moreover, for example, when there is only one secondary transform basiscandidate associated with a primary transform basis candidate determinedas the primary transform basis, processor 160 may avoid encodinginformation indicating the secondary transform basis determined.Furthermore, when a total number of transform basis candidates for oneof information indicating the primary transform basis and informationindicating the secondary transform basis is limited to one, processor160 may encode only the other of the information indicating the primarytransform basis and the information indicating the secondary transformbasis.

Moreover, for example, the secondary transform basis may be a transformbasis equivalent to Karhunen-Loeve transform. In addition, the secondarytransform basis may be a transform basis learned based on the primarytransform basis.

Moreover, for example, when the secondary transform basis is a separabletransform basis, processor 160 may perform a separable transform as thesecondary transform, and when the secondary transform basis is anon-separable transform basis, processor 160 may perform a non-separabletransform as the secondary transform. Furthermore, processor 160 maydetermine whether to perform the secondary transform, and the secondarytransform basis when the secondary transform is performed, based on theprimary transform basis.

Moreover, for example, each of the primary transform and the secondarytransform may be a separable transform or a non-separable transform.

Processor 160 may separate the primary transform into a plurality ofdirectional primary transforms, and may perform the primary transform byperforming the plurality of directional primary transforms.Alternatively, processor 160 may perform the primary transform withoutseparating the primary transform into the plurality of directionalprimary transforms. Moreover, processor 160 may separate the secondarytransform into a plurality of directional secondary transforms, and mayperform the secondary transform by performing the plurality ofdirectional secondary transforms. Alternatively, processor 160 mayperform the secondary transform without separating the secondarytransform into the plurality of directional secondary transforms.

It should be noted that encoder 100 is not limited to theabove-described implementation example, or may include subtractor 104,transformer 106, quantizer 108, and entropy encoder 110. Theseconstituent elements may perform the above-described operations.

For example, subtractor 104 may derive a prediction error by subtractinga prediction image from an image included in a video. Transformer 106may determine a secondary transform basis based on a primary transformbasis. Moreover, transformer 106 may perform a primary transform on theprediction error using the primary transform basis. Furthermore,transformer 106 may perform a secondary transform on the result of theprimary transform using the secondary transform basis.

Quantizer 108 may perform quantization on a result of the secondarytransform. Entropy encoder 110 may encode a result of the quantizationas data of the image.

Further, transformer 106 may perform other operations relating totransform, and entropy encoder 110 may perform other operations relatingto encoding. In addition, transformer 106 may be divided into a primarytransform basis determiner that determines a primary transform basis, aprimary transformer that performs a primary transform, a secondarytransform basis determiner that determines a secondary transform basis,and a secondary transformer that performs a secondary transform.

[Implementation Example of Decoder]

FIG. 26 is a block diagram illustrating an implementation example ofdecoder 200 according to Embodiment 1. Decoder 200 includes processor260 and memory 262. For example, the plurality of constituent elementsof decoder 200 illustrated in FIG. 10 are implemented by processor 260and memory 262 illustrated in FIG. 26 .

Processor 260 is an electronic circuit accessible to memory 262, andperforms information processing. For example, processor 260 is anexclusive or general processor that decodes a video using memory 262.Processor 260 may be a central processing unit (CPU).

Processor 260 may include a plurality of electronic circuits, or mayinclude a plurality of sub-processors. Moreover, processor 260 mayperform the functions of constituent elements among the plurality ofconstituent elements of decoder 200 illustrated in FIG. 10 , except theconstituent elements that store information.

Memory 262 is an exclusive or general memory for storing informationused by processor 260 to decode a video. Memory 262 may be an electroniccircuit, may be connected to processor 260, or may be included inprocessor 260.

Memory 262 may include a plurality of electronic circuits, or mayinclude a plurality of sub-memories. Memory 262 may be a magnetic diskor an optical disc etc., or may be expressed as storage or a recordingmedium etc. Further, memory 262 may be a non-volatile memory or avolatile memory.

Moreover, memory 262 may perform the functions of, among the pluralityof constituent elements of decoder 200 illustrated in FIG. 10 , theconstituent elements that store information. Specifically, memory 262may perform the functions of block memory 210 and frame memory 214illustrated in FIG. 10 .

Memory 262 may store a bitstream corresponding to an encoded video, ormay store a video corresponding to a decoded bitstream. Moreover, memory262 may store a program for causing processor 260 to decode a video.Furthermore, memory 262 may store information etc. indicating anassociation between inverse primary transform basis candidates andinverse secondary transform basis candidates.

It should be noted that not all of the plurality of constituent elementsillustrated in FIG. 10 need to be implemented by decoder 200, and notall of the processes described above need to be performed by decoder200. Some of the plurality of constituent elements illustrated in FIG.10 may be included in another device, and some of the processesdescribed above may be performed by another device. Processing relatingto transform is properly performed by decoder 200 implementing some ofthe plurality of constituent elements illustrated in FIG. 10 andperforming some of the processes described above.

FIG. 27 is a flow chart illustrating an example of operations performedby decoder 200 illustrated in FIG. 26 . For example, decoder 200illustrated in FIG. 26 performs the operations illustrated in FIG. 27when decoder 200 decodes a video.

Specifically, processor 260 decodes data of an image included in a video(S401). Next, processor 260 performs inverse quantization on the data(S402).

Then, processor 260 determines an inverse secondary transform basisbased on an inverse primary transform basis (S403). Next, processor 260performs an inverse secondary transform on the result of the inversequantization using the inverse secondary transform basis (S404). Afterthat, processor 260 performs an inverse primary transform on the resultof the inverse secondary transform using the inverse primary transformbasis (S405). Finally, processor 260 derives the image by adding aresult of the inverse primary transform as a prediction error of theimage to a prediction image of the image (S406).

For example, processor 260 may determine the inverse secondary transformbasis based on the inverse primary transform basis and a parameterdecoded when the processor decodes the video. This parameter may be aparameter indicating an intra prediction mode. In addition, processor260 may determine the inverse secondary transform basis based on theinverse primary transform basis and the intra prediction mode indicatedby the parameter.

Moreover, for example, processor 260 may determine the inverse primarytransform basis from among a plurality of inverse primary transformbasis candidates. Furthermore, processor 260 may determine the inversesecondary transform basis from among at least one inverse secondarytransform basis candidate associated with an inverse primary transformbasis candidate determined as the inverse primary transform basis amongthe plurality of inverse primary transform basis candidates.

Moreover, for example, at least two of the plurality of inverse primarytransform basis candidates may be associated with a common inversesecondary transform basis candidate. Furthermore, a total number of theat least one inverse secondary transform basis candidate associated withthe inverse primary transform basis candidate may depend on the inverseprimary transform basis candidate.

Moreover, for example, the inverse secondary transform basis determinedwhen the inverse primary transform basis is a combination of a firsttransform basis for a vertical direction and a second transform basisfor a horizontal direction may be identical to the inverse secondarytransform basis determined when the inverse primary transform basis is acombination of the second transform basis for the vertical direction andthe first transform basis for the horizontal direction. Furthermore, theinverse secondary transform basis determined when the inverse primarytransform basis is a combination of a first transform basis for avertical direction and a second transform basis for a horizontaldirection may be a transform basis obtained by transposing the inversesecondary transform basis determined when the inverse primary transformbasis is a combination of the second transform basis for the verticaldirection and the first transform basis for the horizontal direction.

Moreover, for example, when the inverse secondary transform basis is acombination of a transform basis for a vertical direction and atransform basis for a horizontal direction, the transform basis for thevertical direction and the transform basis for the horizontal directionmay be identical.

Moreover, for example, processor 260 may decode only one of theinformation indicating the inverse primary transform basis and theinformation indicating the inverse secondary transform basis.

Moreover, for example, when there is only one inverse secondarytransform basis candidate associated with an inverse primary transformbasis candidate determined as the inverse primary transform basis,processor 260 may avoid decoding information indicating the inversesecondary transform basis determined. Furthermore, when a total numberof transform basis candidates for one of information indicating theinverse primary transform basis and information indicating the inversesecondary transform basis is limited to one, processor 260 may decodeonly the other of the information indicating the inverse primarytransform basis and the information indicating the inverse secondarytransform basis.

Moreover, for example, the inverse secondary transform basis may be atransform basis equivalent to Karhunen-Loeve transform. In addition, theinverse secondary transform basis may be a transform basis learned basedon the inverse primary transform basis.

Moreover, for example, when the inverse secondary transform basis is aseparable inverse transform basis, processor 260 may perform a separableinverse transform as the inverse secondary transform, and when theinverse secondary transform basis is a non-separable inverse transformbasis, processor 260 may perform a non-separable inverse transform asthe inverse secondary transform.

Moreover, for example, processor 260 may determine whether to performthe inverse secondary transform, and the inverse secondary transformbasis when the inverse secondary transform is performed, based on theinverse primary transform basis.

Moreover, for example, each of the inverse primary transform and theinverse secondary transform may be a separable inverse transform or anon-separable inverse transform.

Processor 260 may separate the inverse primary transform into aplurality of directional inverse primary transforms, and may perform theinverse primary transform by performing the plurality of directionalinverse primary transforms. Alternatively, processor 260 may perform theinverse primary transform without separating the inverse primarytransform into the plurality of directional inverse primary transforms.Moreover, processor 260 may separate the inverse secondary transforminto a plurality of directional inverse secondary transforms, and mayperform the inverse secondary transform by performing the plurality ofdirectional inverse secondary transforms. Alternatively, processor 260may perform the inverse secondary transform without separating theinverse secondary transform into the plurality of directional inversesecondary transforms.

It should be noted that decoder 200 is not limited to theabove-described implementation example, or may include entropy decoder202, inverse quantizer 204, inverse transformer 206, and adder 208.These constituent elements may perform the above-described operations.

For example, entropy decoder 202 may decode data of an image included ina video. Inverse quantizer 204 may perform inverse quantization on thedata.

Inverse transformer 206 may determine an inverse secondary transformbasis based on an inverse primary transform basis. Moreover, inversetransformer 206 may perform an inverse secondary transform on the resultof the inverse quantization using the inverse secondary transform basis.Furthermore, inverse transformer 206 may perform an inverse primarytransform on the result of the inverse secondary transform using theinverse primary transform basis. Adder 208 may derive the image byadding a result of the inverse primary transform as a prediction errorof the image to a prediction image of the image.

Further, inverse transformer 206 may perform other operations relatingto transform, and entropy decoder 202 may perform other operationsrelating to decoding. In addition, inverse transformer 206 may bedivided into an inverse transform basis determiner that determines aninverse primary transform basis, an inverse primary transformer thatperforms an inverse primary transform, an inverse secondary transformbasis determiner that determines an inverse secondary transform basis,an inverse secondary transformer that performs an inverse secondarytransform, etc.

[Supplemental Information]

Encoder 100 and decoder 200 in the present embodiment may be usedrespectively as an image encoder and an image decoder, or may be usedrespectively as a video encoder and a video decoder. Alternatively,encoder 100 and decoder 200 can be each used as a transformer.

To put it differently, encoder 100 and decoder 200 may correspond onlyto transformer 106 and inverse transformer 206. Other constituentelements such as inter predictor 126 or 218 may be included in anotherdevice.

At least part of the present embodiment may be used as an encodingmethod, may be used as a decoding method, may be used as a transformingmethod, or may be used as another method.

In the present embodiment, each of the constituent elements may beconfigured of dedicated hardware, or may be implemented by executing asoftware program suitable for the constituent element. Each constituentelement may be implemented by a program executor such as a CPU or aprocessor reading and executing a software program recorded on arecording medium such as a hard disk or a semiconductor memory.

Specifically, each of encoder 100 and decoder 200 may include processingcircuitry, and storage electrically connected to the processingcircuitry and accessible from the processing circuitry. For example, theprocessing circuitry corresponds to processor 160 or 260, and thestorage corresponds to memory 162 or 262.

The processing circuitry includes at least one of dedicated hardware ora program executor, and performs processing using the storage. When theprocessing circuitry includes the program executor, the storage stores asoftware program executed by the program executor.

Here, software that implements, for example, encoder 100 or decoder 200according to the present embodiment is a program as follows.

Specifically, the program may cause a computer to execute an encodingmethod of encoding a video, the encoding method including: deriving aprediction error of an image included in the video, by subtracting aprediction image of the image from the image; determining a secondarytransform basis based on a primary transform basis, the primarytransform basis being a transform basis for a primary transform to beperformed on the prediction error, the secondary transform basis being atransform basis for a secondary transform to be performed on a result ofthe primary transform; performing the primary transform on theprediction error using the primary transform basis; performing thesecondary transform on a result of the primary transform using thesecondary transform basis; performing quantization on a result of thesecondary transform; and encoding a result of the quantization as dataof the image.

Alternatively, the program may cause a computer to execute a decodingmethod of decoding a video, the decoding method including: decoding dataof an image included in the video; performing inverse quantization onthe data; determining an inverse secondary transform basis based on aninverse primary transform basis, the inverse primary transform basisbeing a transform basis for an inverse primary transform to be performedon a result of an inverse secondary transform, the inverse secondarytransform basis being a transform basis for the inverse secondarytransform to be performed on a result of the inverse quantization;performing the inverse secondary transform on a result of the inversequantization using the inverse secondary transform basis; performing theinverse primary transform on a result of the inverse secondary transformusing the inverse primary transform basis; and deriving the image byadding a result of the inverse primary transform as a prediction errorof the image to a prediction image of the image.

Each constituent element may be a circuit as described above. Thesecircuits may constitute one circuitry as a whole, or may be separatecircuits. Each constituent element may be implemented by a generalprocessor, or may be implemented by an exclusive processor.

Processing executed by a specific constituent element may be executed byanother constituent element. In addition, the processing execution ordermay be changed, or a plurality of processes may be executed in parallel.An encoding and decoding device may include encoder 100 and decoder 200.

The ordinal numbers such as “first” and “second” used in the descriptionmay be changed as appropriate. A new ordinal number may be given to theconstituent elements, or the ordinal numbers of the constituent elementsmay be removed.

Although aspects of encoder 100 and decoder 200 have been describedabove based on the embodiment, the aspects of encoder 100 and decoder200 are not limited to the embodiment. Various modifications to thepresent embodiment that are conceivable to those skilled in the art, aswell as embodiments resulting from combinations of constituent elementsin different embodiments may be included within the scope of the aspectsof encoder 100 and decoder 200, so long as they do not depart from theessence of the present disclosure.

The present aspect may be implemented in combination with one or more ofthe other aspects in the present disclosure. In addition, part of theprocesses in the flowcharts, part of the constituent elements of theapparatuses, and part of the syntax described in this aspect may beimplemented in combination with other aspects.

Embodiment 2

As described in each of the above embodiments, each functional block cantypically be realized as an MPU and memory, for example. Moreover,processes performed by each of the functional blocks are typicallyrealized by a program execution unit, such as a processor, reading andexecuting software (a program) recorded on a recording medium such asROM. The software may be distributed via, for example, downloading, andmay be recorded on a recording medium such as semiconductor memory anddistributed. Note that each functional block can, of course, also berealized as hardware (dedicated circuit).

Moreover, the processing described in each of the embodiments may berealized via integrated processing using a single apparatus (system),and, alternatively, may be realized via decentralized processing using aplurality of apparatuses. Moreover, the processor that executes theabove-described program may be a single processor or a plurality ofprocessors. In other words, integrated processing may be performed, and,alternatively, decentralized processing may be performed.

Embodiments of the present disclosure are not limited to the aboveexemplary embodiments; various modifications may be made to theexemplary embodiments, the results of which are also included within thescope of the embodiments of the present disclosure.

Next, application examples of the moving picture encoding method (imageencoding method) and the moving picture decoding method (image decodingmethod) described in each of the above embodiments and a system thatemploys the same will be described. The system is characterized asincluding an image encoder that employs the image encoding method, animage decoder that employs the image decoding method, and an imageencoder/decoder that includes both the image encoder and the imagedecoder. Other configurations included in the system may be modified ona case-by-case basis.

Usage Examples

FIG. 28 illustrates an overall configuration of content providing systemex100 for implementing a content distribution service. The area in whichthe communication service is provided is divided into cells of desiredsizes, and base stations ex106, ex107, ex108, ex109, and ex110, whichare fixed wireless stations, are located in respective cells.

In content providing system ex100, devices including computer ex111,gaming device ex112, camera ex113, home appliance ex114, and smartphoneex115 are connected to internet ex101 via internet service providerex102 or communications network ex104 and base stations ex106 throughex110. Content providing system ex100 may combine and connect anycombination of the above elements. The devices may be directly orindirectly connected together via a telephone network or near fieldcommunication rather than via base stations ex106 through ex110, whichare fixed wireless stations. Moreover, streaming server ex103 isconnected to devices including computer ex111, gaming device ex112,camera ex113, home appliance ex114, and smartphone ex115 via, forexample, internet ex101. Streaming server ex103 is also connected to,for example, a terminal in a hotspot in airplane ex117 via satelliteex116.

Note that instead of base stations ex106 through ex110, wireless accesspoints or hotspots may be used. Streaming server ex103 may be connectedto communications network ex104 directly instead of via internet ex101or internet service provider ex102, and may be connected to airplaneex117 directly instead of via satellite ex116.

Camera ex113 is a device capable of capturing still images and video,such as a digital camera. Smartphone ex115 is a smartphone device,cellular phone, or personal handyphone system (PHS) phone that canoperate under the mobile communications system standards of the typical2G, 3G, 3.9G, and 4G systems, as well as the next-generation 5G system.

Home appliance ex118 is, for example, a refrigerator or a deviceincluded in a home fuel cell cogeneration system.

In content providing system ex100, a terminal including an image and/orvideo capturing function is capable of, for example, live streaming byconnecting to streaming server ex103 via, for example, base stationex106. When live streaming, a terminal (e.g., computer ex111, gamingdevice ex112, camera ex113, home appliance ex114, smartphone ex115, orairplane ex117) performs the encoding processing described in the aboveembodiments on still-image or video content captured by a user via theterminal, multiplexes video data obtained via the encoding and audiodata obtained by encoding audio corresponding to the video, andtransmits the obtained data to streaming server ex103. In other words,the terminal functions as the image encoder according to one aspect ofthe present disclosure.

Streaming server ex103 streams transmitted content data to clients thatrequest the stream. Client examples include computer ex111, gamingdevice ex112, camera ex113, home appliance ex114, smartphone ex115, andterminals inside airplane ex117, which are capable of decoding theabove-described encoded data. Devices that receive the streamed datadecode and reproduce the received data. In other words, the devices eachfunction as the image decoder according to one aspect of the presentdisclosure.

[Decentralized Processing]

Streaming server ex103 may be realized as a plurality of servers orcomputers between which tasks such as the processing, recording, andstreaming of data are divided. For example, streaming server ex103 maybe realized as a content delivery network (CDN) that streams content viaa network connecting multiple edge servers located throughout the world.In a CDN, an edge server physically near the client is dynamicallyassigned to the client. Content is cached and streamed to the edgeserver to reduce load times. In the event of, for example, some kind ofan error or a change in connectivity due to, for example, a spike intraffic, it is possible to stream data stably at high speeds since it ispossible to avoid affected parts of the network by, for example,dividing the processing between a plurality of edge servers or switchingthe streaming duties to a different edge server, and continuingstreaming.

Decentralization is not limited to just the division of processing forstreaming; the encoding of the captured data may be divided between andperformed by the terminals, on the server side, or both. In one example,in typical encoding, the processing is performed in two loops. The firstloop is for detecting how complicated the image is on a frame-by-frameor scene-by-scene basis, or detecting the encoding load. The second loopis for processing that maintains image quality and improves encodingefficiency. For example, it is possible to reduce the processing load ofthe terminals and improve the quality and encoding efficiency of thecontent by having the terminals perform the first loop of the encodingand having the server side that received the content perform the secondloop of the encoding. In such a case, upon receipt of a decodingrequest, it is possible for the encoded data resulting from the firstloop performed by one terminal to be received and reproduced on anotherterminal in approximately real time. This makes it possible to realizesmooth, real-time streaming.

In another example, camera ex113 or the like extracts a feature amountfrom an image, compresses data related to the feature amount asmetadata, and transmits the compressed metadata to a server. Forexample, the server determines the significance of an object based onthe feature amount and changes the quantization accuracy accordingly toperform compression suitable for the meaning of the image. Featureamount data is particularly effective in improving the precision andefficiency of motion vector prediction during the second compressionpass performed by the server. Moreover, encoding that has a relativelylow processing load, such as variable length coding (VLC), may behandled by the terminal, and encoding that has a relatively highprocessing load, such as context-adaptive binary arithmetic coding(CABAC), may be handled by the server.

In yet another example, there are instances in which a plurality ofvideos of approximately the same scene are captured by a plurality ofterminals in, for example, a stadium, shopping mall, or factory. In sucha case, for example, the encoding may be decentralized by dividingprocessing tasks between the plurality of terminals that captured thevideos and, if necessary, other terminals that did not capture thevideos and the server, on a per-unit basis. The units may be, forexample, groups of pictures (GOP), pictures, or tiles resulting fromdividing a picture. This makes it possible to reduce load times andachieve streaming that is closer to real-time.

Moreover, since the videos are of approximately the same scene,management and/or instruction may be carried out by the server so thatthe videos captured by the terminals can be cross-referenced. Moreover,the server may receive encoded data from the terminals, change referencerelationship between items of data or correct or replace picturesthemselves, and then perform the encoding. This makes it possible togenerate a stream with increased quality and efficiency for theindividual items of data.

Moreover, the server may stream video data after performing transcodingto convert the encoding format of the video data. For example, theserver may convert the encoding format from MPEG to VP, and may convertH.264 to H.265.

In this way, encoding can be performed by a terminal or one or moreservers. Accordingly, although the device that performs the encoding isreferred to as a “server” or “terminal” in the following description,some or all of the processes performed by the server may be performed bythe terminal, and likewise some or all of the processes performed by theterminal may be performed by the server. This also applies to decodingprocesses.

[3D, Multi-Angle]

In recent years, usage of images or videos combined from images orvideos of different scenes concurrently captured or the same scenecaptured from different angles by a plurality of terminals such ascamera ex113 and/or smartphone ex115 has increased. Videos captured bythe terminals are combined based on, for example, theseparately-obtained relative positional relationship between theterminals, or regions in a video having matching feature points.

In addition to the encoding of two-dimensional moving pictures, theserver may encode a still image based on scene analysis of a movingpicture either automatically or at a point in time specified by theuser, and transmit the encoded still image to a reception terminal.Furthermore, when the server can obtain the relative positionalrelationship between the video capturing terminals, in addition totwo-dimensional moving pictures, the server can generatethree-dimensional geometry of a scene based on video of the same scenecaptured from different angles. Note that the server may separatelyencode three-dimensional data generated from, for example, a pointcloud, and may, based on a result of recognizing or tracking a person orobject using three-dimensional data, select or reconstruct and generatea video to be transmitted to a reception terminal from videos capturedby a plurality of terminals.

This allows the user to enjoy a scene by freely selecting videoscorresponding to the video capturing terminals, and allows the user toenjoy the content obtained by extracting, from three-dimensional datareconstructed from a plurality of images or videos, a video from aselected viewpoint. Furthermore, similar to with video, sound may berecorded from relatively different angles, and the server may multiplex,with the video, audio from a specific angle or space in accordance withthe video, and transmit the result.

In recent years, content that is a composite of the real world and avirtual world, such as virtual reality (VR) and augmented reality (AR)content, has also become popular. In the case of VR images, the servermay create images from the viewpoints of both the left and right eyesand perform encoding that tolerates reference between the two viewpointimages, such as multi-view coding (MVC), and, alternatively, may encodethe images as separate streams without referencing. When the images aredecoded as separate streams, the streams may be synchronized whenreproduced so as to recreate a virtual three-dimensional space inaccordance with the viewpoint of the user.

In the case of AR images, the server superimposes virtual objectinformation existing in a virtual space onto camera informationrepresenting a real-world space, based on a three-dimensional positionor movement from the perspective of the user. The decoder may obtain orstore virtual object information and three-dimensional data, generatetwo-dimensional images based on movement from the perspective of theuser, and then generate superimposed data by seamlessly connecting theimages. Alternatively, the decoder may transmit, to the server, motionfrom the perspective of the user in addition to a request for virtualobject information, and the server may generate superimposed data basedon three-dimensional data stored in the server in accordance with thereceived motion, and encode and stream the generated superimposed datato the decoder. Note that superimposed data includes, in addition to RGBvalues, an α value indicating transparency, and the server sets the avalue for sections other than the object generated fromthree-dimensional data to, for example, 0, and may perform the encodingwhile those sections are transparent. Alternatively, the server may setthe background to a predetermined RGB value, such as a chroma key, andgenerate data in which areas other than the object are set as thebackground.

Decoding of similarly streamed data may be performed by the client(i.e., the terminals), on the server side, or divided therebetween. Inone example, one terminal may transmit a reception request to a server,the requested content may be received and decoded by another terminal,and a decoded signal may be transmitted to a device having a display. Itis possible to reproduce high image quality data by decentralizingprocessing and appropriately selecting content regardless of theprocessing ability of the communications terminal itself. In yet anotherexample, while a TV, for example, is receiving image data that is largein size, a region of a picture, such as a tile obtained by dividing thepicture, may be decoded and displayed on a personal terminal orterminals of a viewer or viewers of the TV. This makes it possible forthe viewers to share a big-picture view as well as for each viewer tocheck his or her assigned area or inspect a region in further detail upclose.

In the future, both indoors and outdoors, in situations in which aplurality of wireless connections are possible over near, mid, and fardistances, it is expected to be able to seamlessly receive content evenwhen switching to data appropriate for the current connection, using astreaming system standard such as MPEG-DASH. With this, the user canswitch between data in real time while freely selecting a decoder ordisplay apparatus including not only his or her own terminal, but also,for example, displays disposed indoors or outdoors. Moreover, based on,for example, information on the position of the user, decoding can beperformed while switching which terminal handles decoding and whichterminal handles the displaying of content. This makes it possible to,while in route to a destination, display, on the wall of a nearbybuilding in which a device capable of displaying content is embedded oron part of the ground, map information while on the move. Moreover, itis also possible to switch the bit rate of the received data based onthe accessibility to the encoded data on a network, such as when encodeddata is cached on a server quickly accessible from the receptionterminal or when encoded data is copied to an edge server in a contentdelivery service.

[Scalable Encoding]

The switching of content will be described with reference to a scalablestream, illustrated in FIG. 29 , that is compression coded viaimplementation of the moving picture encoding method described in theabove embodiments. The server may have a configuration in which contentis switched while making use of the temporal and/or spatial scalabilityof a stream, which is achieved by division into and encoding of layers,as illustrated in FIG. 29 . Note that there may be a plurality ofindividual streams that are of the same content but different quality.In other words, by determining which layer to decode up to based oninternal factors, such as the processing ability on the decoder side,and external factors, such as communication bandwidth, the decoder sidecan freely switch between low resolution content and high resolutioncontent while decoding. For example, in a case in which the user wantsto continue watching, at home on a device such as a TV connected to theinternet, a video that he or she had been previously watching onsmartphone ex115 while on the move, the device can simply decode thesame stream up to a different layer, which reduces server side load.

Furthermore, in addition to the configuration described above in whichscalability is achieved as a result of the pictures being encoded perlayer and the enhancement layer is above the base layer, the enhancementlayer may include metadata based on, for example, statisticalinformation on the image, and the decoder side may generate high imagequality content by performing super-resolution imaging on a picture inthe base layer based on the metadata. Super-resolution imaging may beimproving the SN ratio while maintaining resolution and/or increasingresolution. Metadata includes information for identifying a linear or anon-linear filter coefficient used in super-resolution processing, orinformation identifying a parameter value in filter processing, machinelearning, or least squares method used in super-resolution processing.

Alternatively, a configuration in which a picture is divided into, forexample, tiles in accordance with the meaning of, for example, an objectin the image, and on the decoder side, only a partial region is decodedby selecting a tile to decode, is also acceptable. Moreover, by storingan attribute about the object (person, car, ball, etc.) and a positionof the object in the video (coordinates in identical images) asmetadata, the decoder side can identify the position of a desired objectbased on the metadata and determine which tile or tiles include thatobject. For example, as illustrated in FIG. 30 , metadata is storedusing a data storage structure different from pixel data such as an SEImessage in HEVC. This metadata indicates, for example, the position,size, or color of the main object.

Moreover, metadata may be stored in units of a plurality of pictures,such as stream, sequence, or random access units. With this, the decoderside can obtain, for example, the time at which a specific personappears in the video, and by fitting that with picture unit information,can identify a picture in which the object is present and the positionof the object in the picture.

[Web Page Optimization]

FIG. 31 illustrates an example of a display screen of a web page on, forexample, computer ex111. FIG. 32 illustrates an example of a displayscreen of a web page on, for example, smartphone ex115. As illustratedin FIG. 31 and FIG. 32 , a web page may include a plurality of imagelinks which are links to image content, and the appearance of the webpage differs depending on the device used to view the web page. When aplurality of image links are viewable on the screen, until the userexplicitly selects an image link, or until the image link is in theapproximate center of the screen or the entire image link fits in thescreen, the display apparatus (decoder) displays, as the image links,still images included in the content or I pictures, displays video suchas an animated gif using a plurality of still images or I pictures, forexample, or receives only the base layer and decodes and displays thevideo.

When an image link is selected by the user, the display apparatusdecodes giving the highest priority to the base layer. Note that ifthere is information in the HTML code of the web page indicating thatthe content is scalable, the display apparatus may decode up to theenhancement layer. Moreover, in order to guarantee real timereproduction, before a selection is made or when the bandwidth isseverely limited, the display apparatus can reduce delay between thepoint in time at which the leading picture is decoded and the point intime at which the decoded picture is displayed (that is, the delaybetween the start of the decoding of the content to the displaying ofthe content) by decoding and displaying only forward reference pictures(I picture, P picture, forward reference B picture). Moreover, thedisplay apparatus may purposely ignore the reference relationshipbetween pictures and coarsely decode all B and P pictures as forwardreference pictures, and then perform normal decoding as the number ofpictures received over time increases.

[Autonomous Driving]

When transmitting and receiving still image or video data such two- orthree-dimensional map information for autonomous driving or assisteddriving of an automobile, the reception terminal may receive, inaddition to image data belonging to one or more layers, information on,for example, the weather or road construction as metadata, and associatethe metadata with the image data upon decoding. Note that metadata maybe assigned per layer and, alternatively, may simply be multiplexed withthe image data.

In such a case, since the automobile, drone, airplane, etc., includingthe reception terminal is mobile, the reception terminal can seamlesslyreceive and decode while switching between base stations among basestations ex106 through ex110 by transmitting information indicating theposition of the reception terminal upon reception request. Moreover, inaccordance with the selection made by the user, the situation of theuser, or the bandwidth of the connection, the reception terminal candynamically select to what extent the metadata is received or to whatextent the map information, for example, is updated.

With this, in content providing system ex100, the client can receive,decode, and reproduce, in real time, encoded information transmitted bythe user.

[Streaming of Individual Content]

In content providing system ex100, in addition to high image quality,long content distributed by a video distribution entity, unicast ormulticast streaming of low image quality, short content from anindividual is also possible. Moreover, such content from individuals islikely to further increase in popularity. The server may first performediting processing on the content before the encoding processing inorder to refine the individual content. This may be achieved with, forexample, the following configuration.

In real-time while capturing video or image content or after the contenthas been captured and accumulated, the server performs recognitionprocessing based on the raw or encoded data, such as capture errorprocessing, scene search processing, meaning analysis, and/or objectdetection processing. Then, based on the result of the recognitionprocessing, the server—either when prompted or automatically—edits thecontent, examples of which include: correction such as focus and/ormotion blur correction; removing low-priority scenes such as scenes thatare low in brightness compared to other pictures or out of focus; objectedge adjustment; and color tone adjustment. The server encodes theedited data based on the result of the editing. It is known thatexcessively long videos tend to receive fewer views. Accordingly, inorder to keep the content within a specific length that scales with thelength of the original video, the server may, in addition to thelow-priority scenes described above, automatically clip out scenes withlow movement based on an image processing result. Alternatively, theserver may generate and encode a video digest based on a result of ananalysis of the meaning of a scene.

Note that there are instances in which individual content may includecontent that infringes a copyright, moral right, portrait rights, etc.Such an instance may lead to an unfavorable situation for the creator,such as when content is shared beyond the scope intended by the creator.Accordingly, before encoding, the server may, for example, edit imagesso as to blur faces of people in the periphery of the screen or blur theinside of a house, for example. Moreover, the server may be configuredto recognize the faces of people other than a registered person inimages to be encoded, and when such faces appear in an image, forexample, apply a mosaic filter to the face of the person. Alternatively,as pre- or post-processing for encoding, the user may specify, forcopyright reasons, a region of an image including a person or a regionof the background be processed, and the server may process the specifiedregion by, for example, replacing the region with a different image orblurring the region. If the region includes a person, the person may betracked in the moving picture, and the head region may be replaced withanother image as the person moves.

Moreover, since there is a demand for real-time viewing of contentproduced by individuals, which tends to be small in data size, thedecoder first receives the base layer as the highest priority andperforms decoding and reproduction, although this may differ dependingon bandwidth. When the content is reproduced two or more times, such aswhen the decoder receives the enhancement layer during decoding andreproduction of the base layer and loops the reproduction, the decodermay reproduce a high image quality video including the enhancementlayer. If the stream is encoded using such scalable encoding, the videomay be low quality when in an unselected state or at the start of thevideo, but it can offer an experience in which the image quality of thestream progressively increases in an intelligent manner. This is notlimited to just scalable encoding; the same experience can be offered byconfiguring a single stream from a low quality stream reproduced for thefirst time and a second stream encoded using the first stream as areference.

Other Usage Examples

The encoding and decoding may be performed by Large Scale Integration(LSI) ex500, which is typically included in each terminal. LSI ex500 maybe configured of a single chip or a plurality of chips. Software forencoding and decoding moving pictures may be integrated into some typeof a recording medium (such as a CD-ROM, a flexible disk, or a harddisk) that is readable by, for example, computer ex111, and the encodingand decoding may be performed using the software. Furthermore, whensmartphone ex115 is equipped with a camera, the video data obtained bythe camera may be transmitted. In this case, the video data is coded byLSI ex500 included in smartphone ex115.

Note that LSI ex500 may be configured to download and activate anapplication. In such a case, the terminal first determines whether it iscompatible with the scheme used to encode the content or whether it iscapable of executing a specific service. When the terminal is notcompatible with the encoding scheme of the content or when the terminalis not capable of executing a specific service, the terminal firstdownloads a codec or application software then obtains and reproducesthe content.

Aside from the example of content providing system ex100 that usesinternet ex101, at least the moving picture encoder (image encoder) orthe moving picture decoder (image decoder) described in the aboveembodiments may be implemented in a digital broadcasting system. Thesame encoding processing and decoding processing may be applied totransmit and receive broadcast radio waves superimposed with multiplexedaudio and video data using, for example, a satellite, even though thisis geared toward multicast whereas unicast is easier with contentproviding system ex100.

[Hardware Configuration]

FIG. 33 illustrates smartphone ex115. FIG. 34 illustrates aconfiguration example of smartphone ex115. Smartphone ex115 includesantenna ex450 for transmitting and receiving radio waves to and frombase station ex110, camera ex465 capable of capturing video and stillimages, and display ex458 that displays decoded data, such as videocaptured by camera ex465 and video received by antenna ex450. Smartphoneex115 further includes user interface ex466 such as a touch panel, audiooutput unit ex457 such as a speaker for outputting speech or otheraudio, audio input unit ex456 such as a microphone for audio input,memory ex467 capable of storing decoded data such as captured video orstill images, recorded audio, received video or still images, and mail,as well as decoded data, and slot ex464 which is an interface forSubscriber Identification Module (SIM) ex468 for authorizing access to anetwork and various data. Note that external memory may be used insteadof memory ex467.

Moreover, main controller ex460 which comprehensively controls displayex458 and user interface ex466, power supply circuit ex461, userinterface input controller ex462, video signal processor ex455, camerainterface ex463, display controller ex459, modulator/demodulator ex452,multiplexer/demultiplexer ex453, audio signal processor ex454, slotex464, and memory ex467 are connected via bus ex470.

When the user turns the power button of power supply circuit ex461 on,smartphone ex115 is powered on into an operable state by each componentbeing supplied with power from a battery pack.

Smartphone ex115 performs processing for, for example, calling and datatransmission, based on control performed by main controller ex460, whichincludes a CPU, ROM, and RAM. When making calls, an audio signalrecorded by audio input unit ex456 is converted into a digital audiosignal by audio signal processor ex454, and this is applied with spreadspectrum processing by modulator/demodulator ex452 and digital-analogconversion and frequency conversion processing by transmitter/receiverex451, and then transmitted via antenna ex450. The received data isamplified, frequency converted, and analog-digital converted, inversespread spectrum processed by modulator/demodulator ex452, converted intoan analog audio signal by audio signal processor ex454, and then outputfrom audio output unit ex457. In data transmission mode, text,still-image, or video data is transmitted by main controller ex460 viauser interface input controller ex462 as a result of operation of, forexample, user interface ex466 of the main body, and similar transmissionand reception processing is performed. In data transmission mode, whensending a video, still image, or video and audio, video signal processorex455 compression encodes, via the moving picture encoding methoddescribed in the above embodiments, a video signal stored in memoryex467 or a video signal input from camera ex465, and transmits theencoded video data to multiplexer/demultiplexer ex453. Moreover, audiosignal processor ex454 encodes an audio signal recorded by audio inputunit ex456 while camera ex465 is capturing, for example, a video orstill image, and transmits the encoded audio data tomultiplexer/demultiplexer ex453. Multiplexer/demultiplexer ex453multiplexes the encoded video data and encoded audio data using apredetermined scheme, modulates and converts the data usingmodulator/demodulator (modulator/demodulator circuit) ex452 andtransmitter/receiver ex451, and transmits the result via antenna ex450.

When video appended in an email or a chat, or a video linked from a webpage, for example, is received, in order to decode the multiplexed datareceived via antenna ex450, multiplexer/demultiplexer ex453demultiplexes the multiplexed data to divide the multiplexed data into abitstream of video data and a bitstream of audio data, supplies theencoded video data to video signal processor ex455 via synchronous busex470, and supplies the encoded audio data to audio signal processorex454 via synchronous bus ex470. Video signal processor ex455 decodesthe video signal using a moving picture decoding method corresponding tothe moving picture encoding method described in the above embodiments,and video or a still image included in the linked moving picture file isdisplayed on display ex458 via display controller ex459. Moreover, audiosignal processor ex454 decodes the audio signal and outputs audio fromaudio output unit ex457. Note that since real-time streaming is becomingmore and more popular, there are instances in which reproduction of theaudio may be socially inappropriate depending on the user's environment.Accordingly, as an initial value, a configuration in which only videodata is reproduced, i.e., the audio signal is not reproduced, ispreferable. Audio may be synchronized and reproduced only when an input,such as when the user clicks video data, is received.

Although smartphone ex115 was used in the above example, threeimplementations are conceivable: a transceiver terminal including bothan encoder and a decoder; a transmitter terminal including only anencoder; and a receiver terminal including only a decoder. Further, inthe description of the digital broadcasting system, an example is givenin which multiplexed data obtained as a result of video data beingmultiplexed with, for example, audio data, is received or transmitted,but the multiplexed data may be video data multiplexed with data otherthan audio data, such as text data related to the video. Moreover, thevideo data itself rather than multiplexed data maybe received ortransmitted.

Although main controller ex460 including a CPU is described ascontrolling the encoding or decoding processes, terminals often includeGPUs. Accordingly, a configuration is acceptable in which a large areais processed at once by making use of the performance ability of the GPUvia memory shared by the CPU and GPU or memory including an address thatis managed so as to allow common usage by the CPU and GPU. This makes itpossible to shorten encoding time, maintain the real-time nature of thestream, and reduce delay. In particular, processing relating to motionestimation, deblocking filtering, sample adaptive offset (SAO), andtransformation/quantization can be effectively carried out by the GPUinstead of the CPU in units of, for example pictures, all at once.

Although only some exemplary embodiments of the present disclosure havebeen described in detail above, those skilled in the art will readilyappreciate that many modifications are possible in the exemplaryembodiments without materially departing from the novel teachings andadvantages of the present disclosure. Accordingly, all suchmodifications are intended to be included within the scope of thepresent disclosure.

INDUSTRIAL APPLICABILITY

The present disclosure is applicable to, for example, televisionreceivers, digital video recorders, car navigation systems, mobilephones, digital cameras, digital video cameras, teleconference systems,or electronic mirrors, etc.

What is claimed is:
 1. An encoder comprising: a processor; and memory,wherein, using the memory, the processor: derives a residual signal of acurrent block by subtracting a prediction signal from an input signal;determines an intra prediction mode used for the current block; performsa primary transform on the residual signal, using a primary transformbasis, to generate first transform coefficients; when the primarytransform basis is different from predetermined transform bases,performs a quantization on the first transform coefficients withoutperforming a secondary transform; and when the primary transform basisis included in the predetermined transform bases, (i) performs asecondary transform on the first transform coefficients, using asecondary transform basis selected from among one or more candidatesecondary transform bases associated with the intra prediction mode, togenerate second transform coefficients, and (ii) performs a quantizationon the second transform coefficients, and wherein the secondarytransform is performed on a part of the first transform coefficientsgenerated by the primary transform.
 2. A decoder comprising: aprocessor; and memory, wherein, using the memory, the processor:determines an intra prediction mode used for a current block; determinesan inverse primary transform basis used for an inverse primarytransform; performs an inverse quantization on quantized coefficient ofthe current block to generate second transform coefficients; when theinverse primary transform basis is different from predetermined inversetransform bases, performs the inverse primary transform on the secondtransform coefficients using the inverse primary transform basis withoutperforming an inverse secondary transform, to generate a residual signalof the current block; and when the inverse primary transform basis isincluded in the predetermined inverse transform bases, (i) performs aninverse secondary transform on the second transform coefficients, usingan inverse secondary transform basis selected from among one or morecandidate inverse secondary transform bases associated with the intraprediction mode, to generate first transform coefficients and (ii)performs the inverse primary transform on the first transformcoefficients, using the inverse primary transform basis, to generate aresidual signal of the current block, and wherein the inverse secondarytransform is performed on a part of the second transform coefficientsgenerated by the inverse quantization.